fem_checke_la.c running 
Given du/dx = exp(x)  0<x<1  Boundary u(0) = 1, u(1) = e 
Analytic solution u(x) = exp(x) 
Try 10 points 
x grid and analytic solution 
i=0, Ua( 0.000)= 1.000 
i=1, Ua( 0.111)= 1.118 
i=2, Ua( 0.222)= 1.249 
i=3, Ua( 0.333)= 1.396 
i=4, Ua( 0.444)= 1.560 
i=5, Ua( 0.556)= 1.743 
i=6, Ua( 0.667)= 1.948 
i=7, Ua( 0.778)= 2.177 
i=8, Ua( 0.889)= 2.432 
i=9, Ua( 1.000)= 2.718 

calling gauleg a=0, b=1, np=98 
compute stiffness matrix 
Legendre integration=-1.13471, at i=1, j=0 
adaptive integration=-1.13471, at i=1, j=0 
simple   integration=-1.11702, at i=1, j=0 
Legendre integration=-1.17012e-13, at i=1, j=1 
adaptive integration=-7.63302e-11, at i=1, j=1 
simple   integration=-0.0554713, at i=1, j=1 
Legendre integration=2.70302, at i=1, j=2 
adaptive integration=2.70302, at i=1, j=2 
simple   integration=2.81136, at i=1, j=2 
Legendre integration=-3.58004, at i=1, j=3 
adaptive integration=-3.58004, at i=1, j=3 
simple   integration=-3.74369, at i=1, j=3 
Legendre integration=3.87802, at i=1, j=4 
adaptive integration=3.87802, at i=1, j=4 
simple   integration=4.05466, at i=1, j=4 
Legendre integration=-3.06351, at i=1, j=5 
adaptive integration=-3.06351, at i=1, j=5 
simple   integration=-3.19596, at i=1, j=5 
Legendre integration=1.71222, at i=1, j=6 
adaptive integration=1.71222, at i=1, j=6 
simple   integration=1.77762, at i=1, j=6 
Legendre integration=-0.673845, at i=1, j=7 
adaptive integration=-0.673845, at i=1, j=7 
simple   integration=-0.691863, at i=1, j=7 
Legendre integration=0.265344, at i=1, j=8 
adaptive integration=0.265344, at i=1, j=8 
simple   integration=0.265327, at i=1, j=8 
Legendre integration=-0.106495, at i=1, j=9 
adaptive integration=-0.106495, at i=1, j=9 
simple   integration=-0.10497, at i=1, j=9 
Legendre integration=0.177613, f at i=1 
adaptive integration=0.177613, f at i=1 
simple   integration=0.17715, f at i=1 
Legendre integration=1.71559, at i=2, j=0 
adaptive integration=1.71559, at i=2, j=0 
simple   integration=1.68048, at i=2, j=0 
Legendre integration=-2.70302, at i=2, j=1 
adaptive integration=-2.70302, at i=2, j=1 
simple   integration=-2.59455, at i=2, j=1 
Legendre integration=-4.06883e-13, at i=2, j=2 
adaptive integration=-1.30032e-11, at i=2, j=2 
simple   integration=-0.20588, at i=2, j=2 
Legendre integration=1.96311, at i=2, j=3 
adaptive integration=1.96311, at i=2, j=3 
simple   integration=2.26162, at i=2, j=3 
Legendre integration=-1.88793, at i=2, j=4 
adaptive integration=-1.88793, at i=2, j=4 
simple   integration=-2.18997, at i=2, j=4 
Legendre integration=1.54619, at i=2, j=5 
adaptive integration=1.54619, at i=2, j=5 
simple   integration=1.74748, at i=2, j=5 
Legendre integration=-0.982499, at i=2, j=6 
adaptive integration=-0.982499, at i=2, j=6 
simple   integration=-1.05701, at i=2, j=6 
Legendre integration=0.58646, at i=2, j=7 
adaptive integration=0.58646, at i=2, j=7 
simple   integration=0.586375, at i=2, j=7 
Legendre integration=-0.673845, at i=2, j=8 
adaptive integration=-0.673845, at i=2, j=8 
simple   integration=-0.655729, at i=2, j=8 
Legendre integration=0.435941, at i=2, j=9 
adaptive integration=0.435941, at i=2, j=9 
simple   integration=0.427189, at i=2, j=9 
Legendre integration=0.0938591, f at i=2 
adaptive integration=0.0938591, f at i=2 
simple   integration=0.0941738, f at i=2 
Legendre integration=-2.49546, at i=3, j=0 
adaptive integration=-2.49546, at i=3, j=0 
simple   integration=-2.44133, at i=3, j=0 
Legendre integration=3.58004, at i=3, j=1 
adaptive integration=3.58004, at i=3, j=1 
simple   integration=3.41609, at i=3, j=1 
Legendre integration=-1.96311, at i=3, j=2 
adaptive integration=-1.96311, at i=3, j=2 
simple   integration=-1.66441, at i=3, j=2 
Legendre integration=-7.91936e-13, at i=3, j=3 
adaptive integration=-1.58151e-10, at i=3, j=3 
simple   integration=-0.406004, at i=3, j=3 
Legendre integration=1.54088, at i=3, j=4 
adaptive integration=1.54088, at i=3, j=4 
simple   integration=1.90603, at i=3, j=4 
Legendre integration=-1.20531, at i=3, j=5 
adaptive integration=-1.20531, at i=3, j=5 
simple   integration=-1.38776, at i=3, j=5 
Legendre integration=0.995723, at i=3, j=6 
adaptive integration=0.995723, at i=3, j=6 
simple   integration=0.995544, at i=3, j=6 
Legendre integration=-0.982499, at i=3, j=7 
adaptive integration=-0.982499, at i=3, j=7 
simple   integration=-0.907704, at i=3, j=7 
Legendre integration=1.71222, at i=3, j=8 
adaptive integration=1.71222, at i=3, j=8 
simple   integration=1.64659, at i=3, j=8 
Legendre integration=-1.18248, at i=3, j=9 
adaptive integration=-1.18248, at i=3, j=9 
simple   integration=-1.15704, at i=3, j=9 
Legendre integration=0.107512, f at i=3 
adaptive integration=0.107512, f at i=3 
simple   integration=0.108293, f at i=3 
Legendre integration=2.72653, at i=4, j=0 
adaptive integration=2.72653, at i=4, j=0 
simple   integration=2.66638, at i=4, j=0 
Legendre integration=-3.87802, at i=4, j=1 
adaptive integration=-3.87802, at i=4, j=1 
simple   integration=-3.70097, at i=4, j=1 
Legendre integration=1.88793, at i=4, j=2 
adaptive integration=1.88793, at i=4, j=2 
simple   integration=1.58552, at i=4, j=2 
Legendre integration=-1.54088, at i=4, j=3 
adaptive integration=-1.54088, at i=4, j=3 
simple   integration=-1.17551, at i=4, j=3 
Legendre integration=-4.87404e-13, at i=4, j=4 
adaptive integration=-2.94955e-11, at i=4, j=4 
simple   integration=-0.246457, at i=4, j=4 
Legendre integration=1.38046, at i=4, j=5 
adaptive integration=1.38046, at i=4, j=5 
simple   integration=1.38035, at i=4, j=5 
Legendre integration=-1.20531, at i=4, j=6 
adaptive integration=-1.20531, at i=4, j=6 
simple   integration=-1.0225, at i=4, j=6 
Legendre integration=1.54619, at i=4, j=7 
adaptive integration=1.54619, at i=4, j=7 
simple   integration=1.34451, at i=4, j=7 
Legendre integration=-3.06351, at i=4, j=8 
adaptive integration=-3.06351, at i=4, j=8 
simple   integration=-2.9307, at i=4, j=8 
Legendre integration=2.14661, at i=4, j=9 
adaptive integration=2.14661, at i=4, j=9 
simple   integration=2.09937, at i=4, j=9 
Legendre integration=0.407245, f at i=4 
adaptive integration=0.407245, f at i=4 
simple   integration=0.404364, f at i=4 
Legendre integration=-2.14661, at i=5, j=0 
adaptive integration=-2.14661, at i=5, j=0 
simple   integration=-2.09937, at i=5, j=0 
Legendre integration=3.06351, at i=5, j=1 
adaptive integration=3.06351, at i=5, j=1 
simple   integration=2.9307, at i=5, j=1 
Legendre integration=-1.54619, at i=5, j=2 
adaptive integration=-1.54619, at i=5, j=2 
simple   integration=-1.34451, at i=5, j=2 
Legendre integration=1.20531, at i=5, j=3 
adaptive integration=1.20531, at i=5, j=3 
simple   integration=1.0225, at i=5, j=3 
Legendre integration=-1.38046, at i=5, j=4 
adaptive integration=-1.38046, at i=5, j=4 
simple   integration=-1.38035, at i=5, j=4 
Legendre integration=4.55308e-13, at i=5, j=5 
adaptive integration=2.95391e-11, at i=5, j=5 
simple   integration=0.246457, at i=5, j=5 
Legendre integration=1.54088, at i=5, j=6 
adaptive integration=1.54088, at i=5, j=6 
simple   integration=1.17551, at i=5, j=6 
Legendre integration=-1.88793, at i=5, j=7 
adaptive integration=-1.88793, at i=5, j=7 
simple   integration=-1.58552, at i=5, j=7 
Legendre integration=3.87802, at i=5, j=8 
adaptive integration=3.87802, at i=5, j=8 
simple   integration=3.70097, at i=5, j=8 
Legendre integration=-2.72653, at i=5, j=9 
adaptive integration=-2.72653, at i=5, j=9 
simple   integration=-2.66638, at i=5, j=9 
Legendre integration=-0.211473, f at i=5 
adaptive integration=-0.211473, f at i=5 
simple   integration=-0.206766, f at i=5 
Legendre integration=1.18248, at i=6, j=0 
adaptive integration=1.18248, at i=6, j=0 
simple   integration=1.15704, at i=6, j=0 
Legendre integration=-1.71222, at i=6, j=1 
adaptive integration=-1.71222, at i=6, j=1 
simple   integration=-1.64659, at i=6, j=1 
Legendre integration=0.982499, at i=6, j=2 
adaptive integration=0.982499, at i=6, j=2 
simple   integration=0.907704, at i=6, j=2 
Legendre integration=-0.995723, at i=6, j=3 
adaptive integration=-0.995723, at i=6, j=3 
simple   integration=-0.995544, at i=6, j=3 
Legendre integration=1.20531, at i=6, j=4 
adaptive integration=1.20531, at i=6, j=4 
simple   integration=1.38776, at i=6, j=4 
Legendre integration=-1.54088, at i=6, j=5 
adaptive integration=-1.54088, at i=6, j=5 
simple   integration=-1.90603, at i=6, j=5 
Legendre integration=7.7342e-13, at i=6, j=6 
adaptive integration=1.58184e-10, at i=6, j=6 
simple   integration=0.406004, at i=6, j=6 
Legendre integration=1.96311, at i=6, j=7 
adaptive integration=1.96311, at i=6, j=7 
simple   integration=1.66441, at i=6, j=7 
Legendre integration=-3.58004, at i=6, j=8 
adaptive integration=-3.58004, at i=6, j=8 
simple   integration=-3.41609, at i=6, j=8 
Legendre integration=2.49546, at i=6, j=9 
adaptive integration=2.49546, at i=6, j=9 
simple   integration=2.44133, at i=6, j=9 
Legendre integration=0.648757, f at i=6 
adaptive integration=0.648757, f at i=6 
simple   integration=0.643918, f at i=6 
Legendre integration=-0.435941, at i=7, j=0 
adaptive integration=-0.435941, at i=7, j=0 
simple   integration=-0.427189, at i=7, j=0 
Legendre integration=0.673845, at i=7, j=1 
adaptive integration=0.673845, at i=7, j=1 
simple   integration=0.655729, at i=7, j=1 
Legendre integration=-0.58646, at i=7, j=2 
adaptive integration=-0.58646, at i=7, j=2 
simple   integration=-0.586375, at i=7, j=2 
Legendre integration=0.982499, at i=7, j=3 
adaptive integration=0.982499, at i=7, j=3 
simple   integration=1.05701, at i=7, j=3 
Legendre integration=-1.54619, at i=7, j=4 
adaptive integration=-1.54619, at i=7, j=4 
simple   integration=-1.74748, at i=7, j=4 
Legendre integration=1.88793, at i=7, j=5 
adaptive integration=1.88793, at i=7, j=5 
simple   integration=2.18997, at i=7, j=5 
Legendre integration=-1.96311, at i=7, j=6 
adaptive integration=-1.96311, at i=7, j=6 
simple   integration=-2.26162, at i=7, j=6 
Legendre integration=3.98287e-13, at i=7, j=7 
adaptive integration=1.30196e-11, at i=7, j=7 
simple   integration=0.20588, at i=7, j=7 
Legendre integration=2.70302, at i=7, j=8 
adaptive integration=2.70302, at i=7, j=8 
simple   integration=2.59455, at i=7, j=8 
Legendre integration=-1.71559, at i=7, j=9 
adaptive integration=-1.71559, at i=7, j=9 
simple   integration=-1.68048, at i=7, j=9 
Legendre integration=-0.0772874, f at i=7 
adaptive integration=-0.0772874, f at i=7 
simple   integration=-0.0738747, f at i=7 
Legendre integration=0.106495, at i=8, j=0 
adaptive integration=0.106495, at i=8, j=0 
simple   integration=0.10497, at i=8, j=0 
Legendre integration=-0.265344, at i=8, j=1 
adaptive integration=-0.265344, at i=8, j=1 
simple   integration=-0.265327, at i=8, j=1 
Legendre integration=0.673845, at i=8, j=2 
adaptive integration=0.673845, at i=8, j=2 
simple   integration=0.691863, at i=8, j=2 
Legendre integration=-1.71222, at i=8, j=3 
adaptive integration=-1.71222, at i=8, j=3 
simple   integration=-1.77762, at i=8, j=3 
Legendre integration=3.06351, at i=8, j=4 
adaptive integration=3.06351, at i=8, j=4 
simple   integration=3.19596, at i=8, j=4 
Legendre integration=-3.87802, at i=8, j=5 
adaptive integration=-3.87802, at i=8, j=5 
simple   integration=-4.05466, at i=8, j=5 
Legendre integration=3.58004, at i=8, j=6 
adaptive integration=3.58004, at i=8, j=6 
simple   integration=3.74369, at i=8, j=6 
Legendre integration=-2.70302, at i=8, j=7 
adaptive integration=-2.70302, at i=8, j=7 
simple   integration=-2.81136, at i=8, j=7 
Legendre integration=1.1464e-13, at i=8, j=8 
adaptive integration=7.63317e-11, at i=8, j=8 
simple   integration=0.0554713, at i=8, j=8 
Legendre integration=1.13471, at i=8, j=9 
adaptive integration=1.13471, at i=8, j=9 
simple   integration=1.11702, at i=8, j=9 
Legendre integration=0.454748, f at i=8 
adaptive integration=0.454748, f at i=8 
simple   integration=0.452927, f at i=8 
k computed stiffness matrix 
 1.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000 
-1.135 -0.000  2.703 -3.580  3.878 -3.064  1.712 -0.674  0.265 -0.106 
 1.716 -2.703 -0.000  1.963 -1.888  1.546 -0.982  0.586 -0.674  0.436 
-2.495  3.580 -1.963 -0.000  1.541 -1.205  0.996 -0.982  1.712 -1.182 
 2.727 -3.878  1.888 -1.541 -0.000  1.380 -1.205  1.546 -3.064  2.147 
-2.147  3.064 -1.546  1.205 -1.380  0.000  1.541 -1.888  3.878 -2.727 
 1.182 -1.712  0.982 -0.996  1.205 -1.541  0.000  1.963 -3.580  2.495 
-0.436  0.674 -0.586  0.982 -1.546  1.888 -1.963  0.000  2.703 -1.716 
 0.106 -0.265  0.674 -1.712  3.064 -3.878  3.580 -2.703  0.000  1.135 
 0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  1.000 
f computed forcing function 
 1.000  0.178  0.094  0.108  0.407 -0.211  0.649 -0.077  0.455  2.718 
u computed Galerkin, Ua analytic, error 
u[0]= 1.000, Ua= 1.000, err=2.22045e-16 
u[1]= 1.118, Ua= 1.118, err=1.70952e-12 
u[2]= 1.249, Ua= 1.249, err=3.1477e-12 
u[3]= 1.396, Ua= 1.396, err=1.92579e-12 
u[4]= 1.560, Ua= 1.560, err=2.69629e-12 
u[5]= 1.743, Ua= 1.743, err=2.74691e-12 
u[6]= 1.948, Ua= 1.948, err=1.8936e-12 
u[7]= 2.177, Ua= 2.177, err=3.13305e-12 
u[8]= 2.432, Ua= 2.432, err=1.70752e-12 
u[9]= 2.718, Ua= 2.718, err=0 
                                        maxerr=3.1477e-12, avgerr=1.89606e-12 

kd computed adaptive stiffness matrix 
 1.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000 
-1.135 -0.000  2.703 -3.580  3.878 -3.064  1.712 -0.674  0.265 -0.106 
 1.716 -2.703 -0.000  1.963 -1.888  1.546 -0.982  0.586 -0.674  0.436 
-2.495  3.580 -1.963 -0.000  1.541 -1.205  0.996 -0.982  1.712 -1.182 
 2.727 -3.878  1.888 -1.541 -0.000  1.380 -1.205  1.546 -3.064  2.147 
-2.147  3.064 -1.546  1.205 -1.380  0.000  1.541 -1.888  3.878 -2.727 
 1.182 -1.712  0.982 -0.996  1.205 -1.541  0.000  1.963 -3.580  2.495 
-0.436  0.674 -0.586  0.982 -1.546  1.888 -1.963  0.000  2.703 -1.716 
 0.106 -0.265  0.674 -1.712  3.064 -3.878  3.580 -2.703  0.000  1.135 
 0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  1.000 
fd computed forcing function 
 1.000  0.178  0.094  0.108  0.407 -0.211  0.649 -0.077  0.455  2.718 
ud computed Galerkin, Ua analytic, error 
ud[0]= 1.000, Ua= 1.000, err=0 
ud[1]= 1.118, Ua= 1.118, err=3.87633e-09 
ud[2]= 1.249, Ua= 1.249, err=-6.39612e-10 
ud[3]= 1.396, Ua= 1.396, err=-1.23709e-08 
ud[4]= 1.560, Ua= 1.560, err=-1.34917e-08 
ud[5]= 1.743, Ua= 1.743, err=-1.14328e-08 
ud[6]= 1.948, Ua= 1.948, err=-1.24882e-08 
ud[7]= 2.177, Ua= 2.177, err=-5.40802e-09 
ud[8]= 2.432, Ua= 2.432, err=-1.83388e-09 
ud[9]= 2.718, Ua= 2.718, err=0 
                                        maxerr=1.34917e-08, avgerr=6.15414e-09 


ks computed simple stiffness matrix 
 1.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000 
-1.117 -0.055  2.811 -3.744  4.055 -3.196  1.778 -0.692  0.265 -0.105 
 1.680 -2.595 -0.206  2.262 -2.190  1.747 -1.057  0.586 -0.656  0.427 
-2.441  3.416 -1.664 -0.406  1.906 -1.388  0.996 -0.908  1.647 -1.157 
 2.666 -3.701  1.586 -1.176 -0.246  1.380 -1.022  1.345 -2.931  2.099 
-2.099  2.931 -1.345  1.022 -1.380  0.246  1.176 -1.586  3.701 -2.666 
 1.157 -1.647  0.908 -0.996  1.388 -1.906  0.406  1.664 -3.416  2.441 
-0.427  0.656 -0.586  1.057 -1.747  2.190 -2.262  0.206  2.595 -1.680 
 0.105 -0.265  0.692 -1.778  3.196 -4.055  3.744 -2.811  0.055  1.117 
 0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  1.000 
fs computed forcing function 
 1.000  0.177  0.094  0.108  0.404 -0.207  0.644 -0.074  0.453  2.718 
us computed Galerkin, Ua analytic, error 
us[0]= 1.000, Ua= 1.000, err=-1.22125e-15 
us[1]= 1.118, Ua= 1.118, err=1.92713e-12 
us[2]= 1.249, Ua= 1.249, err=3.34621e-12 
us[3]= 1.396, Ua= 1.396, err=2.14917e-12 
us[4]= 1.560, Ua= 1.560, err=2.90012e-12 
us[5]= 1.743, Ua= 1.743, err=2.95097e-12 
us[6]= 1.948, Ua= 1.948, err=2.1263e-12 
us[7]= 2.177, Ua= 2.177, err=3.34532e-12 
us[8]= 2.432, Ua= 2.432, err=1.94333e-12 
us[9]= 2.718, Ua= 2.718, err=0 
                                        maxerr=3.34621e-12, avgerr=2.06898e-12 


Try 20 points 
x grid and analytic solution 
i=0, Ua( 0.000)= 1.000 
i=1, Ua( 0.053)= 1.054 
i=2, Ua( 0.105)= 1.111 
i=3, Ua( 0.158)= 1.171 
i=4, Ua( 0.211)= 1.234 
i=5, Ua( 0.263)= 1.301 
i=6, Ua( 0.316)= 1.371 
i=7, Ua( 0.368)= 1.445 
i=8, Ua( 0.421)= 1.524 
i=9, Ua( 0.474)= 1.606 
i=10, Ua( 0.526)= 1.693 
i=11, Ua( 0.579)= 1.784 
i=12, Ua( 0.632)= 1.881 
i=13, Ua( 0.684)= 1.982 
i=14, Ua( 0.737)= 2.089 
i=15, Ua( 0.789)= 2.202 
i=16, Ua( 0.842)= 2.321 
i=17, Ua( 0.895)= 2.447 
i=18, Ua( 0.947)= 2.579 
i=19, Ua( 1.000)= 2.718 
i=20, Ua( 1.053)= 2.865 

calling gauleg a=0, b=1, np=64 
compute stiffness matrix 
Legendre integration=-1.77925, at i=1, j=0 
adaptive integration=-1.77925, at i=1, j=0 
simple   integration=-1.58728, at i=1, j=0 
Legendre integration=-2.8682e-12, at i=1, j=1 
adaptive integration=-2.6783e-09, at i=1, j=1 
simple   integration=-0.990198, at i=1, j=1 
Legendre integration=9.25, at i=1, j=2 
adaptive integration=9.25, at i=1, j=2 
simple   integration=13.5994, at i=1, j=2 
Legendre integration=-34.579, at i=1, j=3 
adaptive integration=-34.579, at i=1, j=3 
simple   integration=-50.8149, at i=1, j=3 
Legendre integration=104.128, at i=1, j=4 
adaptive integration=104.128, at i=1, j=4 
simple   integration=152.418, at i=1, j=4 
Legendre integration=-250.53, at i=1, j=5 
adaptive integration=-250.53, at i=1, j=5 
simple   integration=-365.548, at i=1, j=5 
Legendre integration=487.93, at i=1, j=6 
adaptive integration=487.93, at i=1, j=6 
simple   integration=709.896, at i=1, j=6 
Legendre integration=-777.603, at i=1, j=7 
adaptive integration=-777.603, at i=1, j=7 
simple   integration=-1128.1, at i=1, j=7 
Legendre integration=1021.54, at i=1, j=8 
adaptive integration=1021.54, at i=1, j=8 
simple   integration=1477.44, at i=1, j=8 
Legendre integration=-1110.75, at i=1, j=9 
adaptive integration=-1110.75, at i=1, j=9 
simple   integration=-1600.85, at i=1, j=9 
Legendre integration=1000.53, at i=1, j=10 
adaptive integration=1000.53, at i=1, j=10 
simple   integration=1436.06, at i=1, j=10 
Legendre integration=-744.968, at i=1, j=11 
adaptive integration=-744.968, at i=1, j=11 
simple   integration=-1063.82, at i=1, j=11 
Legendre integration=455.903, at i=1, j=12 
adaptive integration=455.903, at i=1, j=12 
simple   integration=646.799, at i=1, j=12 
Legendre integration=-227.101, at i=1, j=13 
adaptive integration=-227.101, at i=1, j=13 
simple   integration=-319.375, at i=1, j=13 
Legendre integration=90.7248, at i=1, j=14 
adaptive integration=90.7248, at i=1, j=14 
simple   integration=125.996, at i=1, j=14 
Legendre integration=-28.4452, at i=1, j=15 
adaptive integration=-28.4452, at i=1, j=15 
simple   integration=-38.7407, at i=1, j=15 
Legendre integration=6.79579, at i=1, j=16 
adaptive integration=6.79579, at i=1, j=16 
simple   integration=8.94272, at i=1, j=16 
Legendre integration=-1.2102, at i=1, j=17 
adaptive integration=-1.2102, at i=1, j=17 
simple   integration=-1.47734, at i=1, j=17 
Legendre integration=0.228706, at i=1, j=18 
adaptive integration=0.228706, at i=1, j=18 
simple   integration=0.227741, at i=1, j=18 
Legendre integration=-0.0762108, at i=1, j=19 
adaptive integration=-0.0762108, at i=1, j=19 
simple   integration=-0.0683691, at i=1, j=19 
Legendre integration=0.111298, f at i=1 
adaptive integration=0.111298, f at i=1 
simple   integration=0.108766, f at i=1 
Legendre integration=6.48374, at i=2, j=0 
adaptive integration=6.48374, at i=2, j=0 
simple   integration=5.62852, at i=2, j=0 
Legendre integration=-9.25, at i=2, j=1 
adaptive integration=-9.25, at i=2, j=1 
simple   integration=-4.86598, at i=2, j=1 
Legendre integration=-3.68817e-11, at i=2, j=2 
adaptive integration=-1.31415e-08, at i=2, j=2 
simple   integration=-19.1451, at i=2, j=2 
Legendre integration=20.1437, at i=2, j=3 
adaptive integration=20.1437, at i=2, j=3 
simple   integration=91.2491, at i=2, j=3 
Legendre integration=-77.2688, at i=2, j=4 
adaptive integration=-77.2688, at i=2, j=4 
simple   integration=-287.613, at i=2, j=4 
Legendre integration=208.383, at i=2, j=5 
adaptive integration=208.383, at i=2, j=5 
simple   integration=706.332, at i=2, j=5 
Legendre integration=-433.481, at i=2, j=6 
adaptive integration=-433.481, at i=2, j=6 
simple   integration=-1387.65, at i=2, j=6 
Legendre integration=721.394, at i=2, j=7 
adaptive integration=721.394, at i=2, j=7 
simple   integration=2215.5, at i=2, j=7 
Legendre integration=-977.716, at i=2, j=8 
adaptive integration=-977.716, at i=2, j=8 
simple   integration=-2901.53, at i=2, j=8 
Legendre integration=1089.21, at i=2, j=9 
adaptive integration=1089.21, at i=2, j=9 
simple   integration=3131.73, at i=2, j=9 
Legendre integration=-1001.42, at i=2, j=10 
adaptive integration=-1001.42, at i=2, j=10 
simple   integration=-2788.02, at i=2, j=10 
Legendre integration=759.937, at i=2, j=11 
adaptive integration=759.937, at i=2, j=11 
simple   integration=2041.13, at i=2, j=11 
Legendre integration=-474.437, at i=2, j=12 
adaptive integration=-474.437, at i=2, j=12 
simple   integration=-1220.08, at i=2, j=12 
Legendre integration=242.163, at i=2, j=13 
adaptive integration=242.163, at i=2, j=13 
simple   integration=588.09, at i=2, j=13 
Legendre integration=-100.219, at i=2, j=14 
adaptive integration=-100.219, at i=2, j=14 
simple   integration=-224.122, at i=2, j=14 
Legendre integration=33.4086, at i=2, j=15 
adaptive integration=33.4086, at i=2, j=15 
simple   integration=65.5142, at i=2, j=15 
Legendre integration=-9.08401, at i=2, j=16 
adaptive integration=-9.08401, at i=2, j=16 
simple   integration=-14.0764, at i=2, j=16 
Legendre integration=2.28822, at i=2, j=17 
adaptive integration=2.28822, at i=2, j=17 
simple   integration=2.26552, at i=2, j=17 
Legendre integration=-1.2102, at i=2, j=18 
adaptive integration=-1.2102, at i=2, j=18 
simple   integration=-0.931505, at i=2, j=18 
Legendre integration=0.678496, at i=2, j=19 
adaptive integration=0.678496, at i=2, j=19 
simple   integration=0.590328, at i=2, j=19 
Legendre integration=-0.126827, f at i=2 
adaptive integration=-0.126827, f at i=2 
simple   integration=-0.117719, f at i=2 
Legendre integration=-23.2615, at i=3, j=0 
adaptive integration=-23.2615, at i=3, j=0 
simple   integration=-20.0448, at i=3, j=0 
Legendre integration=34.579, at i=3, j=1 
adaptive integration=34.579, at i=3, j=1 
simple   integration=18.1555, at i=3, j=1 
Legendre integration=-20.1437, at i=3, j=2 
adaptive integration=-20.1437, at i=3, j=2 
simple   integration=51.216, at i=3, j=2 
Legendre integration=-4.487e-10, at i=3, j=3 
adaptive integration=6.76831e-08, at i=3, j=3 
simple   integration=-263.629, at i=3, j=3 
Legendre integration=78.3223, at i=3, j=4 
adaptive integration=78.3223, at i=3, j=4 
simple   integration=853.501, at i=3, j=4 
Legendre integration=-283.445, at i=3, j=5 
adaptive integration=-283.445, at i=3, j=5 
simple   integration=-2105.68, at i=3, j=5 
Legendre integration=668.978, at i=3, j=6 
adaptive integration=668.978, at i=3, j=6 
simple   integration=4131.73, at i=3, j=6 
Legendre integration=-1196, at i=3, j=7 
adaptive integration=-1196, at i=3, j=7 
simple   integration=-6563.84, at i=3, j=7 
Legendre integration=1700.2, at i=3, j=8 
adaptive integration=1700.2, at i=3, j=8 
simple   integration=8526.25, at i=3, j=8 
Legendre integration=-1963.48, at i=3, j=9 
adaptive integration=-1963.48, at i=3, j=9 
simple   integration=-9097.16, at i=3, j=9 
Legendre integration=1861.37, at i=3, j=10 
adaptive integration=1861.37, at i=3, j=10 
simple   integration=7973.49, at i=3, j=10 
Legendre integration=-1455.16, at i=3, j=11 
adaptive integration=-1455.16, at i=3, j=11 
simple   integration=-5716.04, at i=3, j=11 
Legendre integration=939.312, at i=3, j=12 
adaptive integration=939.312, at i=3, j=12 
simple   integration=3319.43, at i=3, j=12 
Legendre integration=-500.632, at i=3, j=13 
adaptive integration=-500.632, at i=3, j=13 
simple   integration=-1535.38, at i=3, j=13 
Legendre integration=220.799, at i=3, j=14 
adaptive integration=220.799, at i=3, j=14 
simple   integration=549.848, at i=3, j=14 
Legendre integration=-81.6408, at i=3, j=15 
adaptive integration=-81.6408, at i=3, j=15 
simple   integration=-145.257, at i=3, j=15 
Legendre integration=26.5685, at i=3, j=16 
adaptive integration=26.5685, at i=3, j=16 
simple   integration=26.2372, at i=3, j=16 
Legendre integration=-9.08401, at i=3, j=17 
adaptive integration=-9.08401, at i=3, j=17 
simple   integration=-3.90034, at i=3, j=17 
Legendre integration=6.79579, at i=3, j=18 
adaptive integration=6.79579, at i=3, j=18 
simple   integration=4.58813, at i=3, j=18 
Legendre integration=-4.06441, at i=3, j=19 
adaptive integration=-4.06441, at i=3, j=19 
simple   integration=-3.50712, at i=3, j=19 
Legendre integration=0.561377, f at i=3 
adaptive integration=0.561377, f at i=3 
simple   integration=0.536573, f at i=3 
Legendre integration=68.1465, at i=4, j=0 
adaptive integration=68.1465, at i=4, j=0 
simple   integration=58.5241, at i=4, j=0 
Legendre integration=-104.128, at i=4, j=1 
adaptive integration=-104.128, at i=4, j=1 
simple   integration=-55.183, at i=4, j=1 
Legendre integration=77.2688, at i=4, j=2 
adaptive integration=77.2688, at i=4, j=2 
simple   integration=-134.251, at i=4, j=2 
Legendre integration=-78.3223, at i=4, j=3 
adaptive integration=-78.3223, at i=4, j=3 
simple   integration=698.413, at i=4, j=3 
Legendre integration=-3.63674e-09, at i=4, j=4 
adaptive integration=1.10236e-09, at i=4, j=4 
simple   integration=-2267.97, at i=4, j=4 
Legendre integration=295.655, at i=4, j=5 
adaptive integration=295.655, at i=4, j=5 
simple   integration=5582.81, at i=4, j=5 
Legendre integration=-933.978, at i=4, j=6 
adaptive integration=-933.978, at i=4, j=6 
simple   integration=-10880.4, at i=4, j=6 
Legendre integration=1889.22, at i=4, j=7 
adaptive integration=1889.22, at i=4, j=7 
simple   integration=17117.1, at i=4, j=7 
Legendre integration=-2885.48, at i=4, j=8 
adaptive integration=-2885.48, at i=4, j=8 
simple   integration=-21947, at i=4, j=8 
Legendre integration=3505.61, at i=4, j=9 
adaptive integration=3505.61, at i=4, j=9 
simple   integration=23018.7, at i=4, j=9 
Legendre integration=-3466.81, at i=4, j=10 
adaptive integration=-3466.81, at i=4, j=10 
simple   integration=-19719.9, at i=4, j=10 
Legendre integration=2824.63, at i=4, j=11 
adaptive integration=2824.63, at i=4, j=11 
simple   integration=13700, at i=4, j=11 
Legendre integration=-1910.66, at i=4, j=12 
adaptive integration=-1910.66, at i=4, j=12 
simple   integration=-7603.93, at i=4, j=12 
Legendre integration=1080.85, at i=4, j=13 
adaptive integration=1080.85, at i=4, j=13 
simple   integration=3278.79, at i=4, j=13 
Legendre integration=-517.369, at i=4, j=14 
adaptive integration=-517.369, at i=4, j=14 
simple   integration=-1039.27, at i=4, j=14 
Legendre integration=214.7, at i=4, j=15 
adaptive integration=214.7, at i=4, j=15 
simple   integration=211.772, at i=4, j=15 
Legendre integration=-81.6408, at i=4, j=16 
adaptive integration=-81.6408, at i=4, j=16 
simple   integration=-15.9313, at i=4, j=16 
Legendre integration=33.4086, at i=4, j=17 
adaptive integration=33.4086, at i=4, j=17 
simple   integration=0.612138, at i=4, j=17 
Legendre integration=-28.4452, at i=4, j=18 
adaptive integration=-28.4452, at i=4, j=18 
simple   integration=-17.9046, at i=4, j=18 
Legendre integration=17.3324, at i=4, j=19 
adaptive integration=17.3324, at i=4, j=19 
simple   integration=14.8986, at i=4, j=19 
Legendre integration=-0.835792, f at i=4 
adaptive integration=-0.835792, f at i=4 
simple   integration=-0.793889, f at i=4 
Legendre integration=-161.322, at i=5, j=0 
adaptive integration=-161.322, at i=5, j=0 
simple   integration=-138.282, at i=5, j=0 
Legendre integration=250.53, at i=5, j=1 
adaptive integration=250.53, at i=5, j=1 
simple   integration=133.802, at i=5, j=1 
Legendre integration=-208.383, at i=5, j=2 
adaptive integration=-208.383, at i=5, j=2 
simple   integration=293.004, at i=5, j=2 
Legendre integration=283.445, at i=5, j=3 
adaptive integration=283.445, at i=5, j=3 
simple   integration=-1544.86, at i=5, j=3 
Legendre integration=-295.655, at i=5, j=4 
adaptive integration=-295.655, at i=5, j=4 
simple   integration=4998.52, at i=5, j=4 
Legendre integration=-1.89572e-08, at i=5, j=5 
adaptive integration=1.49861e-12, at i=5, j=5 
simple   integration=-12218.4, at i=5, j=5 
Legendre integration=869.749, at i=5, j=6 
adaptive integration=869.749, at i=5, j=6 
simple   integration=23571.3, at i=5, j=6 
Legendre integration=-2361.2, at i=5, j=7 
adaptive integration=-2361.2, at i=5, j=7 
simple   integration=-36573.5, at i=5, j=7 
Legendre integration=4097.62, at i=5, j=8 
adaptive integration=4097.62, at i=5, j=8 
simple   integration=46047.7, at i=5, j=8 
Legendre integration=-5385.86, at i=5, j=9 
adaptive integration=-5385.86, at i=5, j=9 
simple   integration=-47134.7, at i=5, j=9 
Legendre integration=5661.72, at i=5, j=10 
adaptive integration=5661.72, at i=5, j=10 
simple   integration=39040.9, at i=5, j=10 
Legendre integration=-4884.33, at i=5, j=11 
adaptive integration=-4884.33, at i=5, j=11 
simple   integration=-25817.7, at i=5, j=11 
Legendre integration=3514.6, at i=5, j=12 
adaptive integration=3514.6, at i=5, j=12 
simple   integration=13248, at i=5, j=12 
Legendre integration=-2139.37, at i=5, j=13 
adaptive integration=-2139.37, at i=5, j=13 
simple   integration=-4947.63, at i=5, j=13 
Legendre integration=1120.27, at i=5, j=14 
adaptive integration=1120.27, at i=5, j=14 
simple   integration=1104.26, at i=5, j=14 
Legendre integration=-517.369, at i=5, j=15 
adaptive integration=-517.369, at i=5, j=15 
simple   integration=18.8623, at i=5, j=15 
Legendre integration=220.799, at i=5, j=16 
adaptive integration=220.799, at i=5, j=16 
simple   integration=-113.886, at i=5, j=16 
Legendre integration=-100.219, at i=5, j=17 
adaptive integration=-100.219, at i=5, j=17 
simple   integration=25.7121, at i=5, j=17 
Legendre integration=90.7248, at i=5, j=18 
adaptive integration=90.7248, at i=5, j=18 
simple   integration=54.6892, at i=5, j=18 
Legendre integration=-55.7438, at i=5, j=19 
adaptive integration=-55.7438, at i=5, j=19 
simple   integration=-47.8128, at i=5, j=19 
Legendre integration=0.673683, f at i=5 
adaptive integration=0.673683, f at i=5 
simple   integration=0.662129, f at i=5 
Legendre integration=310.889, at i=6, j=0 
adaptive integration=310.889, at i=6, j=0 
simple   integration=266.185, at i=6, j=0 
Legendre integration=-487.93, at i=6, j=1 
adaptive integration=-487.93, at i=6, j=1 
simple   integration=-262.458, at i=6, j=1 
Legendre integration=433.481, at i=6, j=2 
adaptive integration=433.481, at i=6, j=2 
simple   integration=-528.196, at i=6, j=2 
Legendre integration=-668.978, at i=6, j=3 
adaptive integration=-668.978, at i=6, j=3 
simple   integration=2808.72, at i=6, j=3 
Legendre integration=933.978, at i=6, j=4 
adaptive integration=933.978, at i=6, j=4 
simple   integration=-9035.5, at i=6, j=4 
Legendre integration=-869.749, at i=6, j=5 
adaptive integration=-869.749, at i=6, j=5 
simple   integration=21854.5, at i=6, j=5 
Legendre integration=-6.31671e-08, at i=6, j=6 
adaptive integration=-1.97799e-10, at i=6, j=6 
simple   integration=-41561.5, at i=6, j=6 
Legendre integration=1913.55, at i=6, j=7 
adaptive integration=1913.55, at i=6, j=7 
simple   integration=63269.6, at i=6, j=7 
Legendre integration=-4489.61, at i=6, j=8 
adaptive integration=-4489.61, at i=6, j=8 
simple   integration=-77630.8, at i=6, j=8 
Legendre integration=6771.68, at i=6, j=9 
adaptive integration=6771.68, at i=6, j=9 
simple   integration=76645.5, at i=6, j=9 
Legendre integration=-7804.41, at i=6, j=10 
adaptive integration=-7804.41, at i=6, j=10 
simple   integration=-60169, at i=6, j=10 
Legendre integration=7279.39, at i=6, j=11 
adaptive integration=7279.39, at i=6, j=11 
simple   integration=36454.1, at i=6, j=11 
Legendre integration=-5658.42, at i=6, j=12 
adaptive integration=-5658.42, at i=6, j=12 
simple   integration=-15805.3, at i=6, j=12 
Legendre integration=3740, at i=6, j=13 
adaptive integration=3740, at i=6, j=13 
simple   integration=3685.02, at i=6, j=13 
Legendre integration=-2139.37, at i=6, j=14 
adaptive integration=-2139.37, at i=6, j=14 
simple   integration=730.601, at i=6, j=14 
Legendre integration=1080.85, at i=6, j=15 
adaptive integration=1080.85, at i=6, j=15 
simple   integration=-1146.96, at i=6, j=15 
Legendre integration=-500.632, at i=6, j=16 
adaptive integration=-500.632, at i=6, j=16 
simple   integration=546.749, at i=6, j=16 
Legendre integration=242.163, at i=6, j=17 
adaptive integration=242.163, at i=6, j=17 
simple   integration=-108.58, at i=6, j=17 
Legendre integration=-227.101, at i=6, j=18 
adaptive integration=-227.101, at i=6, j=18 
simple   integration=-132.942, at i=6, j=18 
Legendre integration=140.228, at i=6, j=19 
adaptive integration=140.228, at i=6, j=19 
simple   integration=120.117, at i=6, j=19 
Legendre integration=2.30519, f at i=6 
adaptive integration=2.30519, f at i=6 
simple   integration=2.1281, f at i=6 
Legendre integration=-491.78, at i=7, j=0 
adaptive integration=-491.78, at i=7, j=0 
simple   integration=-420.775, at i=7, j=0 
Legendre integration=777.603, at i=7, j=1 
adaptive integration=777.603, at i=7, j=1 
simple   integration=421.31, at i=7, j=1 
Legendre integration=-721.394, at i=7, j=2 
adaptive integration=-721.394, at i=7, j=2 
simple   integration=785.638, at i=7, j=2 
Legendre integration=1196, at i=7, j=3 
adaptive integration=1196, at i=7, j=3 
simple   integration=-4199.32, at i=7, j=3 
Legendre integration=-1889.22, at i=7, j=4 
adaptive integration=-1889.22, at i=7, j=4 
simple   integration=13386.6, at i=7, j=4 
Legendre integration=2361.2, at i=7, j=5 
adaptive integration=2361.2, at i=7, j=5 
simple   integration=-31914.5, at i=7, j=5 
Legendre integration=-1913.55, at i=7, j=6 
adaptive integration=-1913.55, at i=7, j=6 
simple   integration=59495.8, at i=7, j=6 
Legendre integration=-1.32261e-07, at i=7, j=7 
adaptive integration=1.14494e-10, at i=7, j=7 
simple   integration=-88138.6, at i=7, j=7 
Legendre integration=3187.27, at i=7, j=8 
adaptive integration=3187.27, at i=7, j=8 
simple   integration=104050, at i=7, j=8 
Legendre integration=-6581, at i=7, j=9 
adaptive integration=-6581, at i=7, j=9 
simple   integration=-96907.6, at i=7, j=9 
Legendre integration=8834.9, at i=7, j=10 
adaptive integration=8834.9, at i=7, j=10 
simple   integration=68985.6, at i=7, j=10 
Legendre integration=-9185.29, at i=7, j=11 
adaptive integration=-9185.29, at i=7, j=11 
simple   integration=-34274.9, at i=7, j=11 
Legendre integration=7841.49, at i=7, j=12 
adaptive integration=7841.49, at i=7, j=12 
simple   integration=7724.23, at i=7, j=12 
Legendre integration=-5658.42, at i=7, j=13 
adaptive integration=-5658.42, at i=7, j=13 
simple   integration=4655.64, at i=7, j=13 
Legendre integration=3514.6, at i=7, j=14 
adaptive integration=3514.6, at i=7, j=14 
simple   integration=-6319.99, at i=7, j=14 
Legendre integration=-1910.66, at i=7, j=15 
adaptive integration=-1910.66, at i=7, j=15 
simple   integration=3834.96, at i=7, j=15 
Legendre integration=939.312, at i=7, j=16 
adaptive integration=939.312, at i=7, j=16 
simple   integration=-1464.2, at i=7, j=16 
Legendre integration=-474.437, at i=7, j=17 
adaptive integration=-474.437, at i=7, j=17 
simple   integration=280.495, at i=7, j=17 
Legendre integration=455.903, at i=7, j=18 
adaptive integration=455.903, at i=7, j=18 
simple   integration=261.276, at i=7, j=18 
Legendre integration=-282.542, at i=7, j=19 
adaptive integration=-282.542, at i=7, j=19 
simple   integration=-241.818, at i=7, j=19 
Legendre integration=-9.7425, f at i=7 
adaptive integration=-9.7425, f at i=7 
simple   integration=-9.09012, f at i=7 
Legendre integration=642.459, at i=8, j=0 
adaptive integration=642.459, at i=8, j=0 
simple   integration=549.486, at i=8, j=0 
Legendre integration=-1021.54, at i=8, j=1 
adaptive integration=-1021.54, at i=8, j=1 
simple   integration=-557.832, at i=8, j=1 
Legendre integration=977.716, at i=8, j=2 
adaptive integration=977.716, at i=8, j=2 
simple   integration=-964.047, at i=8, j=2 
Legendre integration=-1700.2, at i=8, j=3 
adaptive integration=-1700.2, at i=8, j=3 
simple   integration=5165.77, at i=8, j=3 
Legendre integration=2885.48, at i=8, j=4 
adaptive integration=2885.48, at i=8, j=4 
simple   integration=-16250.8, at i=8, j=4 
Legendre integration=-4097.62, at i=8, j=5 
adaptive integration=-4097.62, at i=8, j=5 
simple   integration=37964.8, at i=8, j=5 
Legendre integration=4489.61, at i=8, j=6 
adaptive integration=4489.61, at i=8, j=6 
simple   integration=-68779, at i=8, j=6 
Legendre integration=-3187.27, at i=8, j=7 
adaptive integration=-3187.27, at i=8, j=7 
simple   integration=97768.3, at i=8, j=7 
Legendre integration=-1.60612e-07, at i=8, j=8 
adaptive integration=-9.64754e-11, at i=8, j=8 
simple   integration=-108309, at i=8, j=8 
Legendre integration=4182.07, at i=8, j=9 
adaptive integration=4182.07, at i=8, j=9 
simple   integration=90390.5, at i=8, j=9 
Legendre integration=-7800.59, at i=8, j=10 
adaptive integration=-7800.59, at i=8, j=10 
simple   integration=-50818.4, at i=8, j=10 
Legendre integration=9572.47, at i=8, j=11 
adaptive integration=9572.47, at i=8, j=11 
simple   integration=9427.89, at i=8, j=11 
Legendre integration=-9185.29, at i=8, j=12 
adaptive integration=-9185.29, at i=8, j=12 
simple   integration=16179.7, at i=8, j=12 
Legendre integration=7279.39, at i=8, j=13 
adaptive integration=7279.39, at i=8, j=13 
simple   integration=-22109.8, at i=8, j=13 
Legendre integration=-4884.33, at i=8, j=14 
adaptive integration=-4884.33, at i=8, j=14 
simple   integration=16188.5, at i=8, j=14 
Legendre integration=2824.63, at i=8, j=15 
adaptive integration=2824.63, at i=8, j=15 
simple   integration=-8127.29, at i=8, j=15 
Legendre integration=-1455.16, at i=8, j=16 
adaptive integration=-1455.16, at i=8, j=16 
simple   integration=2841.47, at i=8, j=16 
Legendre integration=759.937, at i=8, j=17 
adaptive integration=759.937, at i=8, j=17 
simple   integration=-535.925, at i=8, j=17 
Legendre integration=-744.968, at i=8, j=18 
adaptive integration=-744.968, at i=8, j=18 
simple   integration=-420.1, at i=8, j=18 
Legendre integration=463.195, at i=8, j=19 
adaptive integration=463.195, at i=8, j=19 
simple   integration=396.231, at i=8, j=19 
Legendre integration=22.6435, f at i=8 
adaptive integration=22.6435, f at i=8 
simple   integration=21.2127, f at i=8 
Legendre integration=-695.481, at i=9, j=0 
adaptive integration=-695.481, at i=9, j=0 
simple   integration=-594.744, at i=9, j=0 
Legendre integration=1110.75, at i=9, j=1 
adaptive integration=1110.75, at i=9, j=1 
simple   integration=611.963, at i=9, j=1 
Legendre integration=-1089.21, at i=9, j=2 
adaptive integration=-1089.21, at i=9, j=2 
simple   integration=973.694, at i=9, j=2 
Legendre integration=1963.48, at i=9, j=3 
adaptive integration=1963.48, at i=9, j=3 
simple   integration=-5217.1, at i=9, j=3 
Legendre integration=-3505.61, at i=9, j=4 
adaptive integration=-3505.61, at i=9, j=4 
simple   integration=16099.9, at i=9, j=4 
Legendre integration=5385.86, at i=9, j=5 
adaptive integration=5385.86, at i=9, j=5 
simple   integration=-36513, at i=9, j=5 
Legendre integration=-6771.68, at i=9, j=6 
adaptive integration=-6771.68, at i=9, j=6 
simple   integration=63297.5, at i=9, j=6 
Legendre integration=6581, at i=9, j=7 
adaptive integration=6581, at i=9, j=7 
simple   integration=-83940, at i=9, j=7 
Legendre integration=-4182.07, at i=9, j=8 
adaptive integration=-4182.07, at i=9, j=8 
simple   integration=82151.9, at i=9, j=8 
Legendre integration=-7.58795e-08, at i=9, j=9 
adaptive integration=5.98223e-10, at i=9, j=9 
simple   integration=-51537.8, at i=9, j=9 
Legendre integration=4541.83, at i=9, j=10 
adaptive integration=4541.83, at i=9, j=10 
simple   integration=4472.92, at i=9, j=10 
Legendre integration=-7800.59, at i=9, j=11 
adaptive integration=-7800.59, at i=9, j=11 
simple   integration=35452.8, at i=9, j=11 
Legendre integration=8834.9, at i=9, j=12 
adaptive integration=8834.9, at i=9, j=12 
simple   integration=-51579.4, at i=9, j=12 
Legendre integration=-7804.41, at i=9, j=13 
adaptive integration=-7804.41, at i=9, j=13 
simple   integration=44788.2, at i=9, j=13 
Legendre integration=5661.72, at i=9, j=14 
adaptive integration=5661.72, at i=9, j=14 
simple   integration=-27877.3, at i=9, j=14 
Legendre integration=-3466.81, at i=9, j=15 
adaptive integration=-3466.81, at i=9, j=15 
simple   integration=12879, at i=9, j=15 
Legendre integration=1861.37, at i=9, j=16 
adaptive integration=1861.37, at i=9, j=16 
simple   integration=-4295.88, at i=9, j=16 
Legendre integration=-1001.42, at i=9, j=17 
adaptive integration=-1001.42, at i=9, j=17 
simple   integration=804.224, at i=9, j=17 
Legendre integration=1000.53, at i=9, j=18 
adaptive integration=1000.53, at i=9, j=18 
simple   integration=557.051, at i=9, j=18 
Legendre integration=-624.161, at i=9, j=19 
adaptive integration=-624.161, at i=9, j=19 
simple   integration=-533.784, at i=9, j=19 
Legendre integration=-37.0437, f at i=9 
adaptive integration=-37.0437, f at i=9 
simple   integration=-34.7402, f at i=9 
Legendre integration=624.161, at i=10, j=0 
adaptive integration=624.161, at i=10, j=0 
simple   integration=533.784, at i=10, j=0 
Legendre integration=-1000.53, at i=10, j=1 
adaptive integration=-1000.53, at i=10, j=1 
simple   integration=-557.051, at i=10, j=1 
Legendre integration=1001.42, at i=10, j=2 
adaptive integration=1001.42, at i=10, j=2 
simple   integration=-804.224, at i=10, j=2 
Legendre integration=-1861.37, at i=10, j=3 
adaptive integration=-1861.37, at i=10, j=3 
simple   integration=4295.88, at i=10, j=3 
Legendre integration=3466.81, at i=10, j=4 
adaptive integration=3466.81, at i=10, j=4 
simple   integration=-12879, at i=10, j=4 
Legendre integration=-5661.72, at i=10, j=5 
adaptive integration=-5661.72, at i=10, j=5 
simple   integration=27877.3, at i=10, j=5 
Legendre integration=7804.41, at i=10, j=6 
adaptive integration=7804.41, at i=10, j=6 
simple   integration=-44788.2, at i=10, j=6 
Legendre integration=-8834.9, at i=10, j=7 
adaptive integration=-8834.9, at i=10, j=7 
simple   integration=51579.4, at i=10, j=7 
Legendre integration=7800.59, at i=10, j=8 
adaptive integration=7800.59, at i=10, j=8 
simple   integration=-35452.8, at i=10, j=8 
Legendre integration=-4541.83, at i=10, j=9 
adaptive integration=-4541.83, at i=10, j=9 
simple   integration=-4472.92, at i=10, j=9 
Legendre integration=7.72454e-08, at i=10, j=10 
adaptive integration=-2.5519e-09, at i=10, j=10 
simple   integration=51537.8, at i=10, j=10 
Legendre integration=4182.07, at i=10, j=11 
adaptive integration=4182.07, at i=10, j=11 
simple   integration=-82151.9, at i=10, j=11 
Legendre integration=-6581, at i=10, j=12 
adaptive integration=-6581, at i=10, j=12 
simple   integration=83940, at i=10, j=12 
Legendre integration=6771.68, at i=10, j=13 
adaptive integration=6771.68, at i=10, j=13 
simple   integration=-63297.5, at i=10, j=13 
Legendre integration=-5385.86, at i=10, j=14 
adaptive integration=-5385.86, at i=10, j=14 
simple   integration=36513, at i=10, j=14 
Legendre integration=3505.61, at i=10, j=15 
adaptive integration=3505.61, at i=10, j=15 
simple   integration=-16099.9, at i=10, j=15 
Legendre integration=-1963.48, at i=10, j=16 
adaptive integration=-1963.48, at i=10, j=16 
simple   integration=5217.1, at i=10, j=16 
Legendre integration=1089.21, at i=10, j=17 
adaptive integration=1089.21, at i=10, j=17 
simple   integration=-973.694, at i=10, j=17 
Legendre integration=-1110.75, at i=10, j=18 
adaptive integration=-1110.75, at i=10, j=18 
simple   integration=-611.963, at i=10, j=18 
Legendre integration=695.481, at i=10, j=19 
adaptive integration=695.481, at i=10, j=19 
simple   integration=594.744, at i=10, j=19 
Legendre integration=47.4219, f at i=10 
adaptive integration=47.4219, f at i=10 
simple   integration=44.5246, f at i=10 
Legendre integration=-463.195, at i=11, j=0 
adaptive integration=-463.195, at i=11, j=0 
simple   integration=-396.231, at i=11, j=0 
Legendre integration=744.968, at i=11, j=1 
adaptive integration=744.968, at i=11, j=1 
simple   integration=420.1, at i=11, j=1 
Legendre integration=-759.937, at i=11, j=2 
adaptive integration=-759.937, at i=11, j=2 
simple   integration=535.925, at i=11, j=2 
Legendre integration=1455.16, at i=11, j=3 
adaptive integration=1455.16, at i=11, j=3 
simple   integration=-2841.47, at i=11, j=3 
Legendre integration=-2824.63, at i=11, j=4 
adaptive integration=-2824.63, at i=11, j=4 
simple   integration=8127.29, at i=11, j=4 
Legendre integration=4884.33, at i=11, j=5 
adaptive integration=4884.33, at i=11, j=5 
simple   integration=-16188.5, at i=11, j=5 
Legendre integration=-7279.39, at i=11, j=6 
adaptive integration=-7279.39, at i=11, j=6 
simple   integration=22109.8, at i=11, j=6 
Legendre integration=9185.29, at i=11, j=7 
adaptive integration=9185.29, at i=11, j=7 
simple   integration=-16179.7, at i=11, j=7 
Legendre integration=-9572.47, at i=11, j=8 
adaptive integration=-9572.47, at i=11, j=8 
simple   integration=-9427.89, at i=11, j=8 
Legendre integration=7800.59, at i=11, j=9 
adaptive integration=7800.59, at i=11, j=9 
simple   integration=50818.4, at i=11, j=9 
Legendre integration=-4182.07, at i=11, j=10 
adaptive integration=-4182.07, at i=11, j=10 
simple   integration=-90390.5, at i=11, j=10 
Legendre integration=1.62119e-07, at i=11, j=11 
adaptive integration=-5.73594e-10, at i=11, j=11 
simple   integration=108309, at i=11, j=11 
Legendre integration=3187.27, at i=11, j=12 
adaptive integration=3187.27, at i=11, j=12 
simple   integration=-97768.3, at i=11, j=12 
Legendre integration=-4489.61, at i=11, j=13 
adaptive integration=-4489.61, at i=11, j=13 
simple   integration=68779, at i=11, j=13 
Legendre integration=4097.62, at i=11, j=14 
adaptive integration=4097.62, at i=11, j=14 
simple   integration=-37964.8, at i=11, j=14 
Legendre integration=-2885.48, at i=11, j=15 
adaptive integration=-2885.48, at i=11, j=15 
simple   integration=16250.8, at i=11, j=15 
Legendre integration=1700.2, at i=11, j=16 
adaptive integration=1700.2, at i=11, j=16 
simple   integration=-5165.77, at i=11, j=16 
Legendre integration=-977.716, at i=11, j=17 
adaptive integration=-977.716, at i=11, j=17 
simple   integration=964.047, at i=11, j=17 
Legendre integration=1021.54, at i=11, j=18 
adaptive integration=1021.54, at i=11, j=18 
simple   integration=557.832, at i=11, j=18 
Legendre integration=-642.459, at i=11, j=19 
adaptive integration=-642.459, at i=11, j=19 
simple   integration=-549.486, at i=11, j=19 
Legendre integration=-48.1238, f at i=11 
adaptive integration=-48.1238, f at i=11 
simple   integration=-45.2024, f at i=11 
Legendre integration=282.542, at i=12, j=0 
adaptive integration=282.542, at i=12, j=0 
simple   integration=241.818, at i=12, j=0 
Legendre integration=-455.903, at i=12, j=1 
adaptive integration=-455.903, at i=12, j=1 
simple   integration=-261.276, at i=12, j=1 
Legendre integration=474.437, at i=12, j=2 
adaptive integration=474.437, at i=12, j=2 
simple   integration=-280.495, at i=12, j=2 
Legendre integration=-939.312, at i=12, j=3 
adaptive integration=-939.312, at i=12, j=3 
simple   integration=1464.2, at i=12, j=3 
Legendre integration=1910.66, at i=12, j=4 
adaptive integration=1910.66, at i=12, j=4 
simple   integration=-3834.96, at i=12, j=4 
Legendre integration=-3514.6, at i=12, j=5 
adaptive integration=-3514.6, at i=12, j=5 
simple   integration=6319.99, at i=12, j=5 
Legendre integration=5658.42, at i=12, j=6 
adaptive integration=5658.42, at i=12, j=6 
simple   integration=-4655.64, at i=12, j=6 
Legendre integration=-7841.49, at i=12, j=7 
adaptive integration=-7841.49, at i=12, j=7 
simple   integration=-7724.23, at i=12, j=7 
Legendre integration=9185.29, at i=12, j=8 
adaptive integration=9185.29, at i=12, j=8 
simple   integration=34274.9, at i=12, j=8 
Legendre integration=-8834.9, at i=12, j=9 
adaptive integration=-8834.9, at i=12, j=9 
simple   integration=-68985.6, at i=12, j=9 
Legendre integration=6581, at i=12, j=10 
adaptive integration=6581, at i=12, j=10 
simple   integration=96907.6, at i=12, j=10 
Legendre integration=-3187.27, at i=12, j=11 
adaptive integration=-3187.27, at i=12, j=11 
simple   integration=-104050, at i=12, j=11 
Legendre integration=1.3282e-07, at i=12, j=12 
adaptive integration=5.42292e-10, at i=12, j=12 
simple   integration=88138.6, at i=12, j=12 
Legendre integration=1913.55, at i=12, j=13 
adaptive integration=1913.55, at i=12, j=13 
simple   integration=-59495.8, at i=12, j=13 
Legendre integration=-2361.2, at i=12, j=14 
adaptive integration=-2361.2, at i=12, j=14 
simple   integration=31914.5, at i=12, j=14 
Legendre integration=1889.22, at i=12, j=15 
adaptive integration=1889.22, at i=12, j=15 
simple   integration=-13386.6, at i=12, j=15 
Legendre integration=-1196, at i=12, j=16 
adaptive integration=-1196, at i=12, j=16 
simple   integration=4199.32, at i=12, j=16 
Legendre integration=721.394, at i=12, j=17 
adaptive integration=721.394, at i=12, j=17 
simple   integration=-785.638, at i=12, j=17 
Legendre integration=-777.603, at i=12, j=18 
adaptive integration=-777.603, at i=12, j=18 
simple   integration=-421.31, at i=12, j=18 
Legendre integration=491.78, at i=12, j=19 
adaptive integration=491.78, at i=12, j=19 
simple   integration=420.775, at i=12, j=19 
Legendre integration=39.8739, f at i=12 
adaptive integration=39.8739, f at i=12 
simple   integration=37.4862, f at i=12 
Legendre integration=-140.228, at i=13, j=0 
adaptive integration=-140.228, at i=13, j=0 
simple   integration=-120.117, at i=13, j=0 
Legendre integration=227.101, at i=13, j=1 
adaptive integration=227.101, at i=13, j=1 
simple   integration=132.942, at i=13, j=1 
Legendre integration=-242.163, at i=13, j=2 
adaptive integration=-242.163, at i=13, j=2 
simple   integration=108.58, at i=13, j=2 
Legendre integration=500.632, at i=13, j=3 
adaptive integration=500.632, at i=13, j=3 
simple   integration=-546.749, at i=13, j=3 
Legendre integration=-1080.85, at i=13, j=4 
adaptive integration=-1080.85, at i=13, j=4 
simple   integration=1146.96, at i=13, j=4 
Legendre integration=2139.37, at i=13, j=5 
adaptive integration=2139.37, at i=13, j=5 
simple   integration=-730.601, at i=13, j=5 
Legendre integration=-3740, at i=13, j=6 
adaptive integration=-3740, at i=13, j=6 
simple   integration=-3685.02, at i=13, j=6 
Legendre integration=5658.42, at i=13, j=7 
adaptive integration=5658.42, at i=13, j=7 
simple   integration=15805.3, at i=13, j=7 
Legendre integration=-7279.39, at i=13, j=8 
adaptive integration=-7279.39, at i=13, j=8 
simple   integration=-36454.1, at i=13, j=8 
Legendre integration=7804.41, at i=13, j=9 
adaptive integration=7804.41, at i=13, j=9 
simple   integration=60169, at i=13, j=9 
Legendre integration=-6771.68, at i=13, j=10 
adaptive integration=-6771.68, at i=13, j=10 
simple   integration=-76645.5, at i=13, j=10 
Legendre integration=4489.61, at i=13, j=11 
adaptive integration=4489.61, at i=13, j=11 
simple   integration=77630.8, at i=13, j=11 
Legendre integration=-1913.55, at i=13, j=12 
adaptive integration=-1913.55, at i=13, j=12 
simple   integration=-63269.6, at i=13, j=12 
Legendre integration=6.33815e-08, at i=13, j=13 
adaptive integration=1.00202e-10, at i=13, j=13 
simple   integration=41561.5, at i=13, j=13 
Legendre integration=869.749, at i=13, j=14 
adaptive integration=869.749, at i=13, j=14 
simple   integration=-21854.5, at i=13, j=14 
Legendre integration=-933.978, at i=13, j=15 
adaptive integration=-933.978, at i=13, j=15 
simple   integration=9035.5, at i=13, j=15 
Legendre integration=668.978, at i=13, j=16 
adaptive integration=668.978, at i=13, j=16 
simple   integration=-2808.72, at i=13, j=16 
Legendre integration=-433.481, at i=13, j=17 
adaptive integration=-433.481, at i=13, j=17 
simple   integration=528.196, at i=13, j=17 
Legendre integration=487.93, at i=13, j=18 
adaptive integration=487.93, at i=13, j=18 
simple   integration=262.458, at i=13, j=18 
Legendre integration=-310.889, at i=13, j=19 
adaptive integration=-310.889, at i=13, j=19 
simple   integration=-266.185, at i=13, j=19 
Legendre integration=-26.5779, f at i=13 
adaptive integration=-26.5779, f at i=13 
simple   integration=-24.9918, f at i=13 
Legendre integration=55.7438, at i=14, j=0 
adaptive integration=55.7438, at i=14, j=0 
simple   integration=47.8128, at i=14, j=0 
Legendre integration=-90.7248, at i=14, j=1 
adaptive integration=-90.7248, at i=14, j=1 
simple   integration=-54.6892, at i=14, j=1 
Legendre integration=100.219, at i=14, j=2 
adaptive integration=100.219, at i=14, j=2 
simple   integration=-25.7121, at i=14, j=2 
Legendre integration=-220.799, at i=14, j=3 
adaptive integration=-220.799, at i=14, j=3 
simple   integration=113.886, at i=14, j=3 
Legendre integration=517.369, at i=14, j=4 
adaptive integration=517.369, at i=14, j=4 
simple   integration=-18.8623, at i=14, j=4 
Legendre integration=-1120.27, at i=14, j=5 
adaptive integration=-1120.27, at i=14, j=5 
simple   integration=-1104.26, at i=14, j=5 
Legendre integration=2139.37, at i=14, j=6 
adaptive integration=2139.37, at i=14, j=6 
simple   integration=4947.63, at i=14, j=6 
Legendre integration=-3514.6, at i=14, j=7 
adaptive integration=-3514.6, at i=14, j=7 
simple   integration=-13248, at i=14, j=7 
Legendre integration=4884.33, at i=14, j=8 
adaptive integration=4884.33, at i=14, j=8 
simple   integration=25817.7, at i=14, j=8 
Legendre integration=-5661.72, at i=14, j=9 
adaptive integration=-5661.72, at i=14, j=9 
simple   integration=-39040.9, at i=14, j=9 
Legendre integration=5385.86, at i=14, j=10 
adaptive integration=5385.86, at i=14, j=10 
simple   integration=47134.7, at i=14, j=10 
Legendre integration=-4097.62, at i=14, j=11 
adaptive integration=-4097.62, at i=14, j=11 
simple   integration=-46047.7, at i=14, j=11 
Legendre integration=2361.2, at i=14, j=12 
adaptive integration=2361.2, at i=14, j=12 
simple   integration=36573.5, at i=14, j=12 
Legendre integration=-869.749, at i=14, j=13 
adaptive integration=-869.749, at i=14, j=13 
simple   integration=-23571.3, at i=14, j=13 
Legendre integration=1.90102e-08, at i=14, j=14 
adaptive integration=-1.72954e-10, at i=14, j=14 
simple   integration=12218.4, at i=14, j=14 
Legendre integration=295.655, at i=14, j=15 
adaptive integration=295.655, at i=14, j=15 
simple   integration=-4998.52, at i=14, j=15 
Legendre integration=-283.445, at i=14, j=16 
adaptive integration=-283.445, at i=14, j=16 
simple   integration=1544.86, at i=14, j=16 
Legendre integration=208.383, at i=14, j=17 
adaptive integration=208.383, at i=14, j=17 
simple   integration=-293.004, at i=14, j=17 
Legendre integration=-250.53, at i=14, j=18 
adaptive integration=-250.53, at i=14, j=18 
simple   integration=-133.802, at i=14, j=18 
Legendre integration=161.322, at i=14, j=19 
adaptive integration=161.322, at i=14, j=19 
simple   integration=138.282, at i=14, j=19 
Legendre integration=14.6445, f at i=14 
adaptive integration=14.6445, f at i=14 
simple   integration=13.7906, f at i=14 
Legendre integration=-17.3324, at i=15, j=0 
adaptive integration=-17.3324, at i=15, j=0 
simple   integration=-14.8986, at i=15, j=0 
Legendre integration=28.4452, at i=15, j=1 
adaptive integration=28.4452, at i=15, j=1 
simple   integration=17.9046, at i=15, j=1 
Legendre integration=-33.4086, at i=15, j=2 
adaptive integration=-33.4086, at i=15, j=2 
simple   integration=-0.612138, at i=15, j=2 
Legendre integration=81.6408, at i=15, j=3 
adaptive integration=81.6408, at i=15, j=3 
simple   integration=15.9313, at i=15, j=3 
Legendre integration=-214.7, at i=15, j=4 
adaptive integration=-214.7, at i=15, j=4 
simple   integration=-211.772, at i=15, j=4 
Legendre integration=517.369, at i=15, j=5 
adaptive integration=517.369, at i=15, j=5 
simple   integration=1039.27, at i=15, j=5 
Legendre integration=-1080.85, at i=15, j=6 
adaptive integration=-1080.85, at i=15, j=6 
simple   integration=-3278.79, at i=15, j=6 
Legendre integration=1910.66, at i=15, j=7 
adaptive integration=1910.66, at i=15, j=7 
simple   integration=7603.93, at i=15, j=7 
Legendre integration=-2824.63, at i=15, j=8 
adaptive integration=-2824.63, at i=15, j=8 
simple   integration=-13700, at i=15, j=8 
Legendre integration=3466.81, at i=15, j=9 
adaptive integration=3466.81, at i=15, j=9 
simple   integration=19719.9, at i=15, j=9 
Legendre integration=-3505.61, at i=15, j=10 
adaptive integration=-3505.61, at i=15, j=10 
simple   integration=-23018.7, at i=15, j=10 
Legendre integration=2885.48, at i=15, j=11 
adaptive integration=2885.48, at i=15, j=11 
simple   integration=21947, at i=15, j=11 
Legendre integration=-1889.22, at i=15, j=12 
adaptive integration=-1889.22, at i=15, j=12 
simple   integration=-17117.1, at i=15, j=12 
Legendre integration=933.978, at i=15, j=13 
adaptive integration=933.978, at i=15, j=13 
simple   integration=10880.4, at i=15, j=13 
Legendre integration=-295.655, at i=15, j=14 
adaptive integration=-295.655, at i=15, j=14 
simple   integration=-5582.81, at i=15, j=14 
Legendre integration=3.64756e-09, at i=15, j=15 
adaptive integration=-1.11995e-09, at i=15, j=15 
simple   integration=2267.97, at i=15, j=15 
Legendre integration=78.3223, at i=15, j=16 
adaptive integration=78.3223, at i=15, j=16 
simple   integration=-698.413, at i=15, j=16 
Legendre integration=-77.2688, at i=15, j=17 
adaptive integration=-77.2688, at i=15, j=17 
simple   integration=134.251, at i=15, j=17 
Legendre integration=104.128, at i=15, j=18 
adaptive integration=104.128, at i=15, j=18 
simple   integration=55.183, at i=15, j=18 
Legendre integration=-68.1465, at i=15, j=19 
adaptive integration=-68.1465, at i=15, j=19 
simple   integration=-58.5241, at i=15, j=19 
Legendre integration=-6.279, f at i=15 
adaptive integration=-6.279, f at i=15 
simple   integration=-5.90935, f at i=15 
Legendre integration=4.06441, at i=16, j=0 
adaptive integration=4.06441, at i=16, j=0 
simple   integration=3.50712, at i=16, j=0 
Legendre integration=-6.79579, at i=16, j=1 
adaptive integration=-6.79579, at i=16, j=1 
simple   integration=-4.58813, at i=16, j=1 
Legendre integration=9.08401, at i=16, j=2 
adaptive integration=9.08401, at i=16, j=2 
simple   integration=3.90034, at i=16, j=2 
Legendre integration=-26.5685, at i=16, j=3 
adaptive integration=-26.5685, at i=16, j=3 
simple   integration=-26.2372, at i=16, j=3 
Legendre integration=81.6408, at i=16, j=4 
adaptive integration=81.6408, at i=16, j=4 
simple   integration=145.257, at i=16, j=4 
Legendre integration=-220.799, at i=16, j=5 
adaptive integration=-220.799, at i=16, j=5 
simple   integration=-549.848, at i=16, j=5 
Legendre integration=500.632, at i=16, j=6 
adaptive integration=500.632, at i=16, j=6 
simple   integration=1535.38, at i=16, j=6 
Legendre integration=-939.312, at i=16, j=7 
adaptive integration=-939.312, at i=16, j=7 
simple   integration=-3319.43, at i=16, j=7 
Legendre integration=1455.16, at i=16, j=8 
adaptive integration=1455.16, at i=16, j=8 
simple   integration=5716.04, at i=16, j=8 
Legendre integration=-1861.37, at i=16, j=9 
adaptive integration=-1861.37, at i=16, j=9 
simple   integration=-7973.49, at i=16, j=9 
Legendre integration=1963.48, at i=16, j=10 
adaptive integration=1963.48, at i=16, j=10 
simple   integration=9097.16, at i=16, j=10 
Legendre integration=-1700.2, at i=16, j=11 
adaptive integration=-1700.2, at i=16, j=11 
simple   integration=-8526.25, at i=16, j=11 
Legendre integration=1196, at i=16, j=12 
adaptive integration=1196, at i=16, j=12 
simple   integration=6563.84, at i=16, j=12 
Legendre integration=-668.978, at i=16, j=13 
adaptive integration=-668.978, at i=16, j=13 
simple   integration=-4131.73, at i=16, j=13 
Legendre integration=283.445, at i=16, j=14 
adaptive integration=283.445, at i=16, j=14 
simple   integration=2105.68, at i=16, j=14 
Legendre integration=-78.3223, at i=16, j=15 
adaptive integration=-78.3223, at i=16, j=15 
simple   integration=-853.501, at i=16, j=15 
Legendre integration=4.4998e-10, at i=16, j=16 
adaptive integration=-6.76829e-08, at i=16, j=16 
simple   integration=263.629, at i=16, j=16 
Legendre integration=20.1437, at i=16, j=17 
adaptive integration=20.1437, at i=16, j=17 
simple   integration=-51.216, at i=16, j=17 
Legendre integration=-34.579, at i=16, j=18 
adaptive integration=-34.579, at i=16, j=18 
simple   integration=-18.1555, at i=16, j=18 
Legendre integration=23.2615, at i=16, j=19 
adaptive integration=23.2615, at i=16, j=19 
simple   integration=20.0448, at i=16, j=19 
Legendre integration=2.38158, f at i=16 
adaptive integration=2.38158, f at i=16 
simple   integration=2.25426, f at i=16 
Legendre integration=-0.678496, at i=17, j=0 
adaptive integration=-0.678496, at i=17, j=0 
simple   integration=-0.590328, at i=17, j=0 
Legendre integration=1.2102, at i=17, j=1 
adaptive integration=1.2102, at i=17, j=1 
simple   integration=0.931505, at i=17, j=1 
Legendre integration=-2.28822, at i=17, j=2 
adaptive integration=-2.28822, at i=17, j=2 
simple   integration=-2.26552, at i=17, j=2 
Legendre integration=9.08401, at i=17, j=3 
adaptive integration=9.08401, at i=17, j=3 
simple   integration=14.0764, at i=17, j=3 
Legendre integration=-33.4086, at i=17, j=4 
adaptive integration=-33.4086, at i=17, j=4 
simple   integration=-65.5142, at i=17, j=4 
Legendre integration=100.219, at i=17, j=5 
adaptive integration=100.219, at i=17, j=5 
simple   integration=224.122, at i=17, j=5 
Legendre integration=-242.163, at i=17, j=6 
adaptive integration=-242.163, at i=17, j=6 
simple   integration=-588.09, at i=17, j=6 
Legendre integration=474.437, at i=17, j=7 
adaptive integration=474.437, at i=17, j=7 
simple   integration=1220.08, at i=17, j=7 
Legendre integration=-759.937, at i=17, j=8 
adaptive integration=-759.937, at i=17, j=8 
simple   integration=-2041.13, at i=17, j=8 
Legendre integration=1001.42, at i=17, j=9 
adaptive integration=1001.42, at i=17, j=9 
simple   integration=2788.02, at i=17, j=9 
Legendre integration=-1089.21, at i=17, j=10 
adaptive integration=-1089.21, at i=17, j=10 
simple   integration=-3131.73, at i=17, j=10 
Legendre integration=977.716, at i=17, j=11 
adaptive integration=977.716, at i=17, j=11 
simple   integration=2901.53, at i=17, j=11 
Legendre integration=-721.394, at i=17, j=12 
adaptive integration=-721.394, at i=17, j=12 
simple   integration=-2215.5, at i=17, j=12 
Legendre integration=433.481, at i=17, j=13 
adaptive integration=433.481, at i=17, j=13 
simple   integration=1387.65, at i=17, j=13 
Legendre integration=-208.383, at i=17, j=14 
adaptive integration=-208.383, at i=17, j=14 
simple   integration=-706.332, at i=17, j=14 
Legendre integration=77.2688, at i=17, j=15 
adaptive integration=77.2688, at i=17, j=15 
simple   integration=287.613, at i=17, j=15 
Legendre integration=-20.1437, at i=17, j=16 
adaptive integration=-20.1437, at i=17, j=16 
simple   integration=-91.2491, at i=17, j=16 
Legendre integration=3.69456e-11, at i=17, j=17 
adaptive integration=1.31412e-08, at i=17, j=17 
simple   integration=19.1451, at i=17, j=17 
Legendre integration=9.25, at i=17, j=18 
adaptive integration=9.25, at i=17, j=18 
simple   integration=4.86598, at i=17, j=18 
Legendre integration=-6.48374, at i=17, j=19 
adaptive integration=-6.48374, at i=17, j=19 
simple   integration=-5.62852, at i=17, j=19 
Legendre integration=-0.516873, f at i=17 
adaptive integration=-0.516873, f at i=17 
simple   integration=-0.482183, f at i=17 
Legendre integration=0.0762108, at i=18, j=0 
adaptive integration=0.0762108, at i=18, j=0 
simple   integration=0.0683691, at i=18, j=0 
Legendre integration=-0.228706, at i=18, j=1 
adaptive integration=-0.228706, at i=18, j=1 
simple   integration=-0.227741, at i=18, j=1 
Legendre integration=1.2102, at i=18, j=2 
adaptive integration=1.2102, at i=18, j=2 
simple   integration=1.47734, at i=18, j=2 
Legendre integration=-6.79579, at i=18, j=3 
adaptive integration=-6.79579, at i=18, j=3 
simple   integration=-8.94272, at i=18, j=3 
Legendre integration=28.4452, at i=18, j=4 
adaptive integration=28.4452, at i=18, j=4 
simple   integration=38.7407, at i=18, j=4 
Legendre integration=-90.7248, at i=18, j=5 
adaptive integration=-90.7248, at i=18, j=5 
simple   integration=-125.996, at i=18, j=5 
Legendre integration=227.101, at i=18, j=6 
adaptive integration=227.101, at i=18, j=6 
simple   integration=319.375, at i=18, j=6 
Legendre integration=-455.903, at i=18, j=7 
adaptive integration=-455.903, at i=18, j=7 
simple   integration=-646.799, at i=18, j=7 
Legendre integration=744.968, at i=18, j=8 
adaptive integration=744.968, at i=18, j=8 
simple   integration=1063.82, at i=18, j=8 
Legendre integration=-1000.53, at i=18, j=9 
adaptive integration=-1000.53, at i=18, j=9 
simple   integration=-1436.06, at i=18, j=9 
Legendre integration=1110.75, at i=18, j=10 
adaptive integration=1110.75, at i=18, j=10 
simple   integration=1600.85, at i=18, j=10 
Legendre integration=-1021.54, at i=18, j=11 
adaptive integration=-1021.54, at i=18, j=11 
simple   integration=-1477.44, at i=18, j=11 
Legendre integration=777.603, at i=18, j=12 
adaptive integration=777.603, at i=18, j=12 
simple   integration=1128.1, at i=18, j=12 
Legendre integration=-487.93, at i=18, j=13 
adaptive integration=-487.93, at i=18, j=13 
simple   integration=-709.896, at i=18, j=13 
Legendre integration=250.53, at i=18, j=14 
adaptive integration=250.53, at i=18, j=14 
simple   integration=365.548, at i=18, j=14 
Legendre integration=-104.128, at i=18, j=15 
adaptive integration=-104.128, at i=18, j=15 
simple   integration=-152.418, at i=18, j=15 
Legendre integration=34.579, at i=18, j=16 
adaptive integration=34.579, at i=18, j=16 
simple   integration=50.8149, at i=18, j=16 
Legendre integration=-9.25, at i=18, j=17 
adaptive integration=-9.25, at i=18, j=17 
simple   integration=-13.5994, at i=18, j=17 
Legendre integration=2.85856e-12, at i=18, j=18 
adaptive integration=2.6783e-09, at i=18, j=18 
simple   integration=0.990198, at i=18, j=18 
Legendre integration=1.77925, at i=18, j=19 
adaptive integration=1.77925, at i=18, j=19 
simple   integration=1.58728, at i=18, j=19 
Legendre integration=0.300346, f at i=18 
adaptive integration=0.300346, f at i=18 
simple   integration=0.292423, f at i=18 
k computed stiffness matrix 
 1.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000 
-1.779 -0.000  9.250 -34.579 104.128 -250.530 487.930 -777.603 1021.543 -1110.747 1000.535 -744.968 455.903 -227.101 90.725 -28.445  6.796 -1.210  0.229 -0.076 
 6.484 -9.250 -0.000 20.144 -77.269 208.383 -433.481 721.394 -977.716 1089.210 -1001.424 759.937 -474.437 242.163 -100.219 33.409 -9.084  2.288 -1.210  0.678 
-23.261 34.579 -20.144 -0.000 78.322 -283.445 668.978 -1196.002 1700.196 -1963.482 1861.366 -1455.161 939.312 -500.632 220.799 -81.641 26.568 -9.084  6.796 -4.064 
68.146 -104.128 77.269 -78.322 -0.000 295.655 -933.978 1889.221 -2885.484 3505.614 -3466.805 2824.632 -1910.659 1080.852 -517.369 214.700 -81.641 33.409 -28.445 17.332 
-161.322 250.530 -208.383 283.445 -295.655 -0.000 869.749 -2361.201 4097.618 -5385.859 5661.723 -4884.328 3514.595 -2139.375 1120.273 -517.369 220.799 -100.219 90.725 -55.744 
310.889 -487.930 433.481 -668.978 933.978 -869.749 -0.000 1913.546 -4489.612 6771.679 -7804.412 7279.393 -5658.417 3739.998 -2139.375 1080.852 -500.632 242.163 -227.101 140.228 
-491.780 777.603 -721.394 1196.002 -1889.221 2361.201 -1913.546 -0.000 3187.274 -6581.000 8834.899 -9185.286 7841.493 -5658.417 3514.595 -1910.659 939.312 -474.437 455.903 -282.542 
642.459 -1021.543 977.716 -1700.196 2885.484 -4097.618 4489.612 -3187.274 -0.000 4182.065 -7800.590 9572.471 -9185.286 7279.393 -4884.328 2824.632 -1455.161 759.937 -744.968 463.195 
-695.481 1110.747 -1089.210 1963.482 -3505.614 5385.859 -6771.679 6581.000 -4182.065 -0.000 4541.830 -7800.590 8834.899 -7804.412 5661.723 -3466.805 1861.366 -1001.424 1000.535 -624.161 
624.161 -1000.535 1001.424 -1861.366 3466.805 -5661.723 7804.412 -8834.899 7800.590 -4541.830  0.000 4182.065 -6581.000 6771.679 -5385.859 3505.614 -1963.482 1089.210 -1110.747 695.481 
-463.195 744.968 -759.937 1455.161 -2824.632 4884.328 -7279.393 9185.286 -9572.471 7800.590 -4182.065  0.000 3187.274 -4489.612 4097.618 -2885.484 1700.196 -977.716 1021.543 -642.459 
282.542 -455.903 474.437 -939.312 1910.659 -3514.595 5658.417 -7841.493 9185.286 -8834.899 6581.000 -3187.274  0.000 1913.546 -2361.201 1889.221 -1196.002 721.394 -777.603 491.780 
-140.228 227.101 -242.163 500.632 -1080.852 2139.375 -3739.998 5658.417 -7279.393 7804.412 -6771.679 4489.612 -1913.546  0.000 869.749 -933.978 668.978 -433.481 487.930 -310.889 
55.744 -90.725 100.219 -220.799 517.369 -1120.273 2139.375 -3514.595 4884.328 -5661.723 5385.859 -4097.618 2361.201 -869.749  0.000 295.655 -283.445 208.383 -250.530 161.322 
-17.332 28.445 -33.409 81.641 -214.700 517.369 -1080.852 1910.659 -2824.632 3466.805 -3505.614 2885.484 -1889.221 933.978 -295.655  0.000 78.322 -77.269 104.128 -68.146 
 4.064 -6.796  9.084 -26.568 81.641 -220.799 500.632 -939.312 1455.161 -1861.366 1963.482 -1700.196 1196.002 -668.978 283.445 -78.322  0.000 20.144 -34.579 23.261 
-0.678  1.210 -2.288  9.084 -33.409 100.219 -242.163 474.437 -759.937 1001.424 -1089.210 977.716 -721.394 433.481 -208.383 77.269 -20.144  0.000  9.250 -6.484 
 0.076 -0.229  1.210 -6.796 28.445 -90.725 227.101 -455.903 744.968 -1000.535 1110.747 -1021.543 777.603 -487.930 250.530 -104.128 34.579 -9.250  0.000  1.779 
 0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  1.000 
f computed forcing function 
 1.000  0.111 -0.127  0.561 -0.836  0.674  2.305 -9.742 22.643 -37.044 47.422 -48.124 39.874 -26.578 14.645 -6.279  2.382 -0.517  0.300  2.718 
u computed Galerkin, Ua analytic, error 
u[0]= 1.000, Ua= 1.000, err=-2.367e-13 
u[1]= 1.054, Ua= 1.054, err=2.75697e-10 
u[2]= 1.111, Ua= 1.111, err=2.02337e-10 
u[3]= 1.171, Ua= 1.171, err=2.91594e-10 
u[4]= 1.234, Ua= 1.234, err=2.23607e-10 
u[5]= 1.301, Ua= 1.301, err=2.39949e-10 
u[6]= 1.371, Ua= 1.371, err=2.97499e-10 
u[7]= 1.445, Ua= 1.445, err=1.9899e-10 
u[8]= 1.524, Ua= 1.524, err=1.10165e-10 
u[9]= 1.606, Ua= 1.606, err=-2.1227e-11 
u[10]= 1.693, Ua= 1.693, err=-1.11345e-10 
u[11]= 1.784, Ua= 1.784, err=-1.55551e-11 
u[12]= 1.881, Ua= 1.881, err=-7.95286e-11 
u[13]= 1.982, Ua= 1.982, err=-3.4109e-10 
u[14]= 2.089, Ua= 2.089, err=-3.20749e-10 
u[15]= 2.202, Ua= 2.202, err=-3.01824e-10 
u[16]= 2.321, Ua= 2.321, err=-3.8155e-10 
u[17]= 2.447, Ua= 2.447, err=-2.57503e-10 
u[18]= 2.579, Ua= 2.579, err=-3.53671e-10 
u[19]= 2.718, Ua= 2.718, err=0 
                                        maxerr=3.8155e-10, avgerr=2.01206e-10 

kd computed adaptive stiffness matrix 
 1.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000 
-1.779 -0.000  9.250 -34.579 104.128 -250.530 487.930 -777.603 1021.543 -1110.747 1000.535 -744.968 455.903 -227.101 90.725 -28.445  6.796 -1.210  0.229 -0.076 
 6.484 -9.250 -0.000 20.144 -77.269 208.383 -433.481 721.394 -977.716 1089.210 -1001.424 759.937 -474.437 242.163 -100.219 33.409 -9.084  2.288 -1.210  0.678 
-23.261 34.579 -20.144  0.000 78.322 -283.445 668.978 -1196.002 1700.196 -1963.482 1861.366 -1455.161 939.312 -500.632 220.799 -81.641 26.568 -9.084  6.796 -4.064 
68.146 -104.128 77.269 -78.322  0.000 295.655 -933.978 1889.221 -2885.484 3505.614 -3466.805 2824.632 -1910.659 1080.852 -517.369 214.700 -81.641 33.409 -28.445 17.332 
-161.322 250.530 -208.383 283.445 -295.655  0.000 869.749 -2361.201 4097.618 -5385.859 5661.723 -4884.328 3514.595 -2139.375 1120.273 -517.369 220.799 -100.219 90.725 -55.744 
310.889 -487.930 433.481 -668.978 933.978 -869.749 -0.000 1913.546 -4489.612 6771.679 -7804.412 7279.393 -5658.417 3739.998 -2139.375 1080.852 -500.632 242.163 -227.101 140.228 
-491.780 777.603 -721.394 1196.002 -1889.221 2361.201 -1913.546  0.000 3187.274 -6581.000 8834.899 -9185.286 7841.493 -5658.417 3514.595 -1910.659 939.312 -474.437 455.903 -282.542 
642.459 -1021.543 977.716 -1700.196 2885.484 -4097.618 4489.612 -3187.274 -0.000 4182.065 -7800.590 9572.471 -9185.286 7279.393 -4884.328 2824.632 -1455.161 759.937 -744.968 463.195 
-695.481 1110.747 -1089.210 1963.482 -3505.614 5385.859 -6771.679 6581.000 -4182.065  0.000 4541.830 -7800.590 8834.899 -7804.412 5661.723 -3466.805 1861.366 -1001.424 1000.535 -624.161 
624.161 -1000.535 1001.424 -1861.366 3466.805 -5661.723 7804.412 -8834.899 7800.590 -4541.830 -0.000 4182.065 -6581.000 6771.679 -5385.859 3505.614 -1963.482 1089.210 -1110.747 695.481 
-463.195 744.968 -759.937 1455.161 -2824.632 4884.328 -7279.393 9185.286 -9572.471 7800.590 -4182.065 -0.000 3187.274 -4489.612 4097.618 -2885.484 1700.196 -977.716 1021.543 -642.459 
282.542 -455.903 474.437 -939.312 1910.659 -3514.595 5658.417 -7841.493 9185.286 -8834.899 6581.000 -3187.274  0.000 1913.546 -2361.201 1889.221 -1196.002 721.394 -777.603 491.780 
-140.228 227.101 -242.163 500.632 -1080.852 2139.375 -3739.998 5658.417 -7279.393 7804.412 -6771.679 4489.612 -1913.546  0.000 869.749 -933.978 668.978 -433.481 487.930 -310.889 
55.744 -90.725 100.219 -220.799 517.369 -1120.273 2139.375 -3514.595 4884.328 -5661.723 5385.859 -4097.618 2361.201 -869.749 -0.000 295.655 -283.445 208.383 -250.530 161.322 
-17.332 28.445 -33.409 81.641 -214.700 517.369 -1080.852 1910.659 -2824.632 3466.805 -3505.614 2885.484 -1889.221 933.978 -295.655 -0.000 78.322 -77.269 104.128 -68.146 
 4.064 -6.796  9.084 -26.568 81.641 -220.799 500.632 -939.312 1455.161 -1861.366 1963.482 -1700.196 1196.002 -668.978 283.445 -78.322 -0.000 20.144 -34.579 23.261 
-0.678  1.210 -2.288  9.084 -33.409 100.219 -242.163 474.437 -759.937 1001.424 -1089.210 977.716 -721.394 433.481 -208.383 77.269 -20.144  0.000  9.250 -6.484 
 0.076 -0.229  1.210 -6.796 28.445 -90.725 227.101 -455.903 744.968 -1000.535 1110.747 -1021.543 777.603 -487.930 250.530 -104.128 34.579 -9.250  0.000  1.779 
 0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  1.000 
fd computed forcing function 
 1.000  0.111 -0.127  0.561 -0.836  0.674  2.305 -9.742 22.643 -37.044 47.422 -48.124 39.874 -26.578 14.645 -6.279  2.382 -0.517  0.300  2.718 
ud computed Galerkin, Ua analytic, error 
ud[0]= 1.000, Ua= 1.000, err=-1.31228e-13 
ud[1]= 1.054, Ua= 1.054, err=1.94862e-06 
ud[2]= 1.111, Ua= 1.111, err=1.13743e-06 
ud[3]= 1.171, Ua= 1.171, err=2.54575e-06 
ud[4]= 1.234, Ua= 1.234, err=8.37142e-07 
ud[5]= 1.301, Ua= 1.301, err=-1.94314e-06 
ud[6]= 1.371, Ua= 1.371, err=-2.42072e-06 
ud[7]= 1.445, Ua= 1.445, err=-1.58962e-06 
ud[8]= 1.524, Ua= 1.524, err=-4.25314e-07 
ud[9]= 1.606, Ua= 1.606, err=-3.10682e-07 
ud[10]= 1.693, Ua= 1.693, err=-5.07252e-07 
ud[11]= 1.784, Ua= 1.784, err=-4.05703e-07 
ud[12]= 1.881, Ua= 1.881, err=-2.53518e-06 
ud[13]= 1.982, Ua= 1.982, err=-5.37507e-06 
ud[14]= 2.089, Ua= 2.089, err=-4.14624e-06 
ud[15]= 2.202, Ua= 2.202, err=-2.52542e-06 
ud[16]= 2.321, Ua= 2.321, err=-2.79549e-06 
ud[17]= 2.447, Ua= 2.447, err=-1.87411e-06 
ud[18]= 2.579, Ua= 2.579, err=-2.59799e-06 
ud[19]= 2.718, Ua= 2.718, err=0 
                                        maxerr=5.37507e-06, avgerr=1.79604e-06 

ks computed simple stiffness matrix 
 1.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000 
-1.587 -0.990 13.599 -50.815 152.418 -365.548 709.896 -1128.101 1477.435 -1600.849 1436.061 -1063.822 646.799 -319.375 125.996 -38.741  8.943 -1.477  0.228 -0.068 
 5.629 -4.866 -19.145 91.249 -287.613 706.332 -1387.648 2215.504 -2901.531 3131.727 -2788.019 2041.127 -1220.076 588.090 -224.122 65.514 -14.076  2.266 -0.932  0.590 
-20.045 18.156 51.216 -263.629 853.501 -2105.678 4131.728 -6563.843 8526.251 -9097.164 7973.489 -5716.040 3319.433 -1535.385 549.848 -145.257 26.237 -3.900  4.588 -3.507 
58.524 -55.183 -134.251 698.413 -2267.966 5582.813 -10880.363 17117.081 -21946.973 23018.709 -19719.865 13700.024 -7603.926 3278.788 -1039.271 211.772 -15.931  0.612 -17.905 14.899 
-138.282 133.802 293.004 -1544.861 4998.522 -12218.366 23571.300 -36573.505 46047.728 -47134.698 39040.861 -25817.708 13248.009 -4947.628 1104.258 18.862 -113.886 25.712 54.689 -47.813 
266.185 -262.458 -528.196 2808.715 -9035.499 21854.527 -41561.455 63269.632 -77630.752 76645.465 -60169.040 36454.133 -15805.260 3685.018 730.601 -1146.959 546.749 -108.580 -132.942 120.117 
-420.775 421.310 785.638 -4199.323 13386.626 -31914.496 59495.790 -88138.569 104050.061 -96907.560 68985.607 -34274.909 7724.230 4655.643 -6319.992 3834.964 -1464.196 280.495 261.276 -241.818 
549.486 -557.832 -964.047 5165.773 -16250.819 37964.764 -68779.032 97768.320 -108309.463 90390.485 -50818.359 9427.888 16179.686 -22109.781 16188.538 -8127.286 2841.475 -535.925 -420.100 396.231 
-594.744 611.963 973.694 -5217.096 16099.908 -36512.997 63297.488 -83940.008 82151.854 -51537.834 4472.924 35452.810 -51579.439 44788.175 -27877.295 12878.983 -4295.877 804.224 557.051 -533.784 
533.784 -557.051 -804.224 4295.877 -12878.983 27877.295 -44788.175 51579.439 -35452.810 -4472.924 51537.834 -82151.854 83940.008 -63297.488 36512.997 -16099.908 5217.096 -973.694 -611.963 594.744 
-396.231 420.100 535.925 -2841.475 8127.286 -16188.538 22109.781 -16179.686 -9427.888 50818.359 -90390.485 108309.463 -97768.320 68779.032 -37964.764 16250.819 -5165.773 964.047 557.832 -549.486 
241.818 -261.276 -280.495 1464.196 -3834.964 6319.992 -4655.643 -7724.230 34274.909 -68985.607 96907.560 -104050.061 88138.569 -59495.790 31914.496 -13386.626 4199.323 -785.638 -421.310 420.775 
-120.117 132.942 108.580 -546.749 1146.959 -730.601 -3685.018 15805.260 -36454.133 60169.040 -76645.465 77630.752 -63269.632 41561.455 -21854.527 9035.499 -2808.715 528.196 262.458 -266.185 
47.813 -54.689 -25.712 113.886 -18.862 -1104.258 4947.628 -13248.009 25817.708 -39040.861 47134.698 -46047.728 36573.505 -23571.300 12218.366 -4998.522 1544.861 -293.004 -133.802 138.282 
-14.899 17.905 -0.612 15.931 -211.772 1039.271 -3278.788 7603.926 -13700.024 19719.865 -23018.709 21946.973 -17117.081 10880.363 -5582.813 2267.966 -698.413 134.251 55.183 -58.524 
 3.507 -4.588  3.900 -26.237 145.257 -549.848 1535.385 -3319.433 5716.040 -7973.489 9097.164 -8526.251 6563.843 -4131.728 2105.678 -853.501 263.629 -51.216 -18.156 20.045 
-0.590  0.932 -2.266 14.076 -65.514 224.122 -588.090 1220.076 -2041.127 2788.019 -3131.727 2901.531 -2215.504 1387.648 -706.332 287.613 -91.249 19.145  4.866 -5.629 
 0.068 -0.228  1.477 -8.943 38.741 -125.996 319.375 -646.799 1063.822 -1436.061 1600.849 -1477.435 1128.101 -709.896 365.548 -152.418 50.815 -13.599  0.990  1.587 
 0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  1.000 
fs computed forcing function 
 1.000  0.109 -0.118  0.537 -0.794  0.662  2.128 -9.090 21.213 -34.740 44.525 -45.202 37.486 -24.992 13.791 -5.909  2.254 -0.482  0.292  2.718 
us computed Galerkin, Ua analytic, error 
us[0]= 1.000, Ua= 1.000, err=5.35683e-12 
us[1]= 1.054, Ua= 1.054, err=-5.00141e-10 
us[2]= 1.111, Ua= 1.111, err=-4.59019e-10 
us[3]= 1.171, Ua= 1.171, err=-5.02568e-10 
us[4]= 1.234, Ua= 1.234, err=-4.7693e-10 
us[5]= 1.301, Ua= 1.301, err=-4.33745e-10 
us[6]= 1.371, Ua= 1.371, err=-4.55715e-10 
us[7]= 1.445, Ua= 1.445, err=-4.92723e-10 
us[8]= 1.524, Ua= 1.524, err=-4.72371e-10 
us[9]= 1.606, Ua= 1.606, err=-1.6627e-10 
us[10]= 1.693, Ua= 1.693, err=2.64213e-10 
us[11]= 1.784, Ua= 1.784, err=5.15217e-10 
us[12]= 1.881, Ua= 1.881, err=7.33035e-10 
us[13]= 1.982, Ua= 1.982, err=8.93431e-10 
us[14]= 2.089, Ua= 2.089, err=7.80317e-10 
us[15]= 2.202, Ua= 2.202, err=8.13914e-10 
us[16]= 2.321, Ua= 2.321, err=8.74418e-10 
us[17]= 2.447, Ua= 2.447, err=7.65084e-10 
us[18]= 2.579, Ua= 2.579, err=8.2738e-10 
us[19]= 2.718, Ua= 2.718, err=0 
                                        maxerr=8.93431e-10, avgerr=5.21592e-10