pde_nl13.c running second order, third degree nonlinear 
solve x^2 u''(x) + 2x u'(x) + 3u(x) = f(x)
  f(x) = (41.0/3.0)-(2116.0/9.0)*x +(4780.0/3.0)*x*x - 
         (48976.0/9.0)*x*x*x + 9984.0*x*x*x*x - 
         (88064.0/9.0)*x*x*x*x*x + (14336.0/3.0)*x*x*x*x*x*x -
         (8192.0/9.0)*x*x*x*x*x*x*x) 
 
  0<x<1  Boundary u(0) = 1, u(1) = 1 
Analytic solution u(x) = 1 -(20/3)*x +12*x^2 -(16/3)*x^3 
nx=5, xmin=0.000000, xmax=1.000000, hx=0.250000 
F forcing function and exact solution 
i=0, F(  0.000)= 13.667, exact=  1.000 
i=1, F(  0.250)=  0.000, exact= -0.000 
i=2, F(  0.500)=  0.000, exact= -0.000 
i=3, F(  0.750)=  3.833, exact=  0.500 
i=4, F(  1.000)= -2.333, exact=  1.000 

k[ 0][ 0]=1 
F(0.000000)=1, for f at i=0 
k[ 4][ 4]=1 
F(1.000000)=1, for f at i=4 
compute non linear stiffness matrix 
k[ 1][ 1]=1.66667 
k[ 1][ 5]=6.66667 
k[ 1][ 8]=12 
k[ 1][10]=-4 
k[ 1][11]=-26.6667 
k[ 1][14]=8 
k[ 1][17]=5.33333 
F(0.250000)=4.71845e-16, for f at i=1 
k[ 2][ 2]=3 
k[ 2][ 6]=-2.66667 
k[ 2][ 8]=-5.33333 
k[ 2][ 9]=5.33333 
k[ 2][12]=21.3333 
k[ 2][15]=-40 
k[ 2][18]=21.3333 
F(0.500000)=4.08562e-14, for f at i=2 
k[ 3][ 3]=4.33333 
k[ 3][ 7]=20 
k[ 3][ 9]=-12 
k[ 3][10]=4 
k[ 3][13]=5.33333 
k[ 3][16]=8 
k[ 3][19]=-26.6667 
F(0.750000)=3.83333, for f at i=3 
k computed non linear stiffness matrix, see above 
f computed forcing function, see above 

simeq_newton3 running 
simeq_newton3 itr=0, prev=1e+12, residual=6.83333 
simeq_newton3 itr=1, prev=6.83333, residual=6.052 
simeq_newton3 itr=2, prev=6.052, residual=6.35323 
simeq_newton3 itr=3, prev=6.35323, residual=5.98196 
simeq_newton3 itr=4, prev=5.98196, residual=5.12909 
simeq_newton3 itr=5, prev=5.12909, residual=4.08543 
simeq_newton3 finished 
u computed solution, Ua analytic, error 
u[0]= 1.0000, Ua= 1.0000, err=0 
u[1]= 0.5561, Ua=-0.0000, err=0.556143 
u[2]= 0.2936, Ua=-0.0000, err=0.293607 
u[3]= 0.5023, Ua= 0.5000, err=0.00233826 
u[4]= 1.0000, Ua= 1.0000, err=0 
                                        maxerr=0.556143, avgerr=0.170418 

check_soln on computed solution against PDE 
check_soln 
i= 1, err=0.798979 
i= 2, err=1.50086 
i= 3, err=0.698823 
check_soln max error=1.50086 

just checking check_soln when given correct solution 
check_soln 
i= 1, err=-4.48715e-16 
i= 2, err=-4.14853e-14 
i= 3, err=-2.32259e-13 
check_soln max error=2.32259e-13 

just checking simeq_newton3 when given correct solution 
simeq_newton3 running 
simeq_newton3 itr=0, prev=1e+12, residual=2.75363e-13 
simeq_newton3 finished 
pde_nl13.c finished