corner0.f90 running differential equation to solve d^2u/dx^2 + d^2u/dy^2 = 0 uniform grid on rectangle -1.0,1.0 to -1.0,1.0 known solution to test method omega = 2 Pi alpha = Pi/omega theta = atan2(y,x) 0..2Pi r = sqrt(x^2+y^2) u(x,y) = r^alpha * sin(alpha*theta) xmin= -1.00000000000000 xmax= 1.00000000000000 nx= 11 ymin= -1.00000000000000 ymax= 1.00000000000000 ny= 11 start at 1424116.39100000 seconds xg( 1 )= -1.00000000000000 xg( 2 )= -0.800000000000000 xg( 3 )= -0.600000000000000 xg( 4 )= -0.400000000000000 xg( 5 )= -0.200000000000000 xg( 6 )= 5.551115123125783E-017 xg( 7 )= 0.200000000000000 xg( 8 )= 0.400000000000000 xg( 9 )= 0.600000000000000 xg( 10 )= 0.800000000000000 xg( 11 )= 1.00000000000000 yg( 1 )= -1.00000000000000 yg( 2 )= -0.800000000000000 yg( 3 )= -0.600000000000000 yg( 4 )= -0.400000000000000 yg( 5 )= -0.200000000000000 yg( 6 )= 5.551115123125783E-017 yg( 7 )= 0.200000000000000 yg( 8 )= 0.400000000000000 yg( 9 )= 0.600000000000000 yg( 10 )= 0.800000000000000 yg( 11 )= 1.00000000000000 x= 1.00, y= 0.00, U(x,y)= 0.00000000 x= 1.00, y= 1.00, U(x,y)= 0.45508986 x= 0.00, y= 1.00, U(x,y)= 0.70710678 x=-1.00, y= 1.00, U(x,y)= 1.09868411 x=-1.00, y= 0.00, U(x,y)= 1.00000000 x=-1.00, y=-1.00, U(x,y)= 1.09868411 x= 0.00, y=-1.00, U(x,y)= 0.70710678 x= 1.00, y=-1.00, U(x,y)= 0.45508986 internal cells zeroed matrix initialized i= 2 ,j= 2 is bad err= -1.048709564693340E-002 i= 2 ,j= 3 is bad err= -4.166430984884784E-002 i= 2 ,j= 4 is bad err= -0.365952883697741 i= 2 ,j= 5 is bad err= -4.07708031535127 i= 2 ,j= 6 is bad err= -93.9234857586030 i= 2 ,j= 7 is bad err= -4.07708031535130 i= 2 ,j= 8 is bad err= -0.365952883697529 i= 2 ,j= 9 is bad err= -4.166430984846237E-002 i= 2 ,j= 10 is bad err= -1.048709564357253E-002 i= 3 ,j= 2 is bad err= -3.215108637143516E-002 i= 3 ,j= 3 is bad err= 1.211046825000928E-002 i= 3 ,j= 4 is bad err= 6.052648017840245E-002 i= 3 ,j= 5 is bad err= 0.692390530736415 i= 3 ,j= 6 is bad err= 15.6442286894868 i= 3 ,j= 7 is bad err= 0.692390530736413 i= 3 ,j= 8 is bad err= 6.052648017859374E-002 i= 3 ,j= 9 is bad err= 1.211046825036366E-002 i= 3 ,j= 10 is bad err= -3.215108636850417E-002 i= 4 ,j= 2 is bad err= -0.330396407837741 i= 4 ,j= 3 is bad err= 5.183344401899248E-002 i= 4 ,j= 4 is bad err= -3.127087635400716E-002 i= 4 ,j= 5 is bad err= -0.153737298548821 i= 4 ,j= 6 is bad err= -2.55224737489110 i= 4 ,j= 7 is bad err= -0.153737298548826 i= 4 ,j= 8 is bad err= -3.127087635385792E-002 i= 4 ,j= 9 is bad err= 5.183344401928325E-002 i= 4 ,j= 10 is bad err= -0.330396407835211 i= 5 ,j= 2 is bad err= -4.31949735597020 i= 5 ,j= 3 is bad err= 0.721935457720960 i= 5 ,j= 4 is bad err= -0.187164929330367 i= 5 ,j= 5 is bad err= 0.156919733489787 i= 5 ,j= 6 is bad err= -6.96686315676131 i= 5 ,j= 7 is bad err= 0.156919733489775 i= 5 ,j= 8 is bad err= -0.187164929330196 i= 5 ,j= 9 is bad err= 0.721935457721123 i= 5 ,j= 10 is bad err= -4.31949735596841 i= 6 ,j= 2 is bad err= -123.873713079173 i= 6 ,j= 3 is bad err= 20.6033228452413 i= 6 ,j= 4 is bad err= -3.80208218565005 i= 6 ,j= 5 is bad err= -5.99580089308950 i= 6 ,j= 6 is bad err= 37.5042110405205 i= 6 ,j= 7 is bad err= -5.99580089308952 i= 6 ,j= 8 is bad err= -3.80208218564840 i= 6 ,j= 9 is bad err= 20.6033228452392 i= 6 ,j= 10 is bad err= -123.873713079177 i= 7 ,j= 2 is bad err= -63.5258008524828 i= 7 ,j= 3 is bad err= 10.5866377944086 i= 7 ,j= 4 is bad err= -2.14980707103171 i= 7 ,j= 5 is bad err= -1.30295802445841 i= 7 ,j= 6 is bad err= 12.0564549596567 i= 7 ,j= 7 is bad err= -1.30295802445842 i= 7 ,j= 8 is bad err= -2.14980707103084 i= 7 ,j= 9 is bad err= 10.5866377944075 i= 7 ,j= 10 is bad err= -63.5258008524847 i= 8 ,j= 2 is bad err= -43.5684082955141 i= 8 ,j= 3 is bad err= 7.25800683600795 i= 8 ,j= 4 is bad err= -1.48119677964810 i= 8 ,j= 5 is bad err= -1.13725256834900 i= 8 ,j= 6 is bad err= 7.23351375316173 i= 8 ,j= 7 is bad err= -1.13725256834901 i= 8 ,j= 8 is bad err= -1.48119677964747 i= 8 ,j= 9 is bad err= 7.25800683600721 i= 8 ,j= 10 is bad err= -43.5684082955153 i= 9 ,j= 2 is bad err= -35.0696756219482 i= 9 ,j= 3 is bad err= 5.84192408753860 i= 9 ,j= 4 is bad err= -1.16975876671596 i= 9 ,j= 5 is bad err= -0.519136918410615 i= 9 ,j= 6 is bad err= 21.7763953422882 i= 9 ,j= 7 is bad err= -0.519136918410602 i= 9 ,j= 8 is bad err= -1.16975876671549 i= 9 ,j= 9 is bad err= 5.84192408753804 i= 9 ,j= 10 is bad err= -35.0696756219491 i= 10 ,j= 2 is bad err= -30.2180309094229 i= 10 ,j= 3 is bad err= 5.02901655111958 i= 10 ,j= 4 is bad err= -1.11974079241408 i= 10 ,j= 5 is bad err= -2.76844456523969 i= 10 ,j= 6 is bad err= -74.0668021664657 i= 10 ,j= 7 is bad err= -2.76844456523974 i= 10 ,j= 8 is bad err= -1.11974079241373 i= 10 ,j= 9 is bad err= 5.02901655111912 i= 10 ,j= 10 is bad err= -30.2180309094236 solving took 0.029 seconds check_soln against PDE check soln against PDE max error= 1.358032436504786E-011 exact solution u, computed us, error xg=-0.800, yg=-0.800, u= 0.983, us= 0.995, err= -0.1227534E-01 xg=-0.800, yg=-0.600, u= 0.949, us= 0.975, err= -0.2587019E-01 xg=-0.800, yg=-0.400, u= 0.920, us= 0.958, err= -0.3724855E-01 xg=-0.800, yg=-0.200, u= 0.901, us= 0.947, err= -0.4540614E-01 xg=-0.800, yg= 0.000, u= 0.894, us= 0.943, err= -0.4855090E-01 xg=-0.800, yg= 0.200, u= 0.901, us= 0.947, err= -0.4540614E-01 xg=-0.800, yg= 0.400, u= 0.920, us= 0.958, err= -0.3724855E-01 xg=-0.800, yg= 0.600, u= 0.949, us= 0.975, err= -0.2587019E-01 xg=-0.800, yg= 0.800, u= 0.983, us= 0.995, err= -0.1227534E-01 xg=-0.600, yg=-0.800, u= 0.894, us= 0.921, err= -0.2644158E-01 xg=-0.600, yg=-0.600, u= 0.851, us= 0.904, err= -0.5275859E-01 xg=-0.600, yg=-0.400, u= 0.813, us= 0.890, err= -0.7738907E-01 xg=-0.600, yg=-0.200, u= 0.785, us= 0.881, err= -0.9622950E-01 xg=-0.600, yg= 0.000, u= 0.775, us= 0.878, err= -0.1035469E+00 xg=-0.600, yg= 0.200, u= 0.785, us= 0.881, err= -0.9622950E-01 xg=-0.600, yg= 0.400, u= 0.813, us= 0.890, err= -0.7738907E-01 xg=-0.600, yg= 0.600, u= 0.851, us= 0.904, err= -0.5275859E-01 xg=-0.600, yg= 0.800, u= 0.894, us= 0.921, err= -0.2644158E-01 xg=-0.400, yg=-0.800, u= 0.804, us= 0.844, err= -0.3990948E-01 xg=-0.400, yg=-0.600, u= 0.749, us= 0.830, err= -0.8110929E-01 xg=-0.400, yg=-0.400, u= 0.695, us= 0.818, err= -0.1228736E+00 xg=-0.400, yg=-0.200, u= 0.651, us= 0.810, err= -0.1589589E+00 xg=-0.400, yg= 0.000, u= 0.632, us= 0.807, err= -0.1745920E+00 xg=-0.400, yg= 0.200, u= 0.651, us= 0.810, err= -0.1589589E+00 xg=-0.400, yg= 0.400, u= 0.695, us= 0.818, err= -0.1228736E+00 xg=-0.400, yg= 0.600, u= 0.749, us= 0.830, err= -0.8110929E-01 xg=-0.400, yg= 0.800, u= 0.804, us= 0.844, err= -0.3990948E-01 xg=-0.200, yg=-0.800, u= 0.716, us= 0.767, err= -0.5170036E-01 xg=-0.200, yg=-0.600, u= 0.645, us= 0.753, err= -0.1080507E+00 xg=-0.200, yg=-0.400, u= 0.569, us= 0.741, err= -0.1722556E+00 xg=-0.200, yg=-0.200, u= 0.491, us= 0.733, err= -0.2417587E+00 xg=-0.200, yg= 0.000, u= 0.447, us= 0.730, err= -0.2830894E+00 xg=-0.200, yg= 0.200, u= 0.491, us= 0.733, err= -0.2417587E+00 xg=-0.200, yg= 0.400, u= 0.569, us= 0.741, err= -0.1722556E+00 xg=-0.200, yg= 0.600, u= 0.645, us= 0.753, err= -0.1080507E+00 xg=-0.200, yg= 0.800, u= 0.716, us= 0.767, err= -0.5170036E-01 xg= 0.000, yg=-0.800, u= 0.632, us= 0.691, err= -0.5859416E-01 xg= 0.000, yg=-0.600, u= 0.548, us= 0.674, err= -0.1265549E+00 xg= 0.000, yg=-0.400, u= 0.447, us= 0.660, err= -0.2130913E+00 xg= 0.000, yg=-0.200, u= 0.316, us= 0.651, err= -0.3348358E+00 xg= 0.000, yg= 0.000, u= 0.000, us= 0.648, err= -0.6478207E+00 xg= 0.000, yg= 0.200, u= 0.316, us= 0.651, err= -0.3348358E+00 xg= 0.000, yg= 0.400, u= 0.447, us= 0.660, err= -0.2130913E+00 xg= 0.000, yg= 0.600, u= 0.548, us= 0.674, err= -0.1265549E+00 xg= 0.000, yg= 0.800, u= 0.632, us= 0.691, err= -0.5859416E-01 xg= 0.200, yg=-0.800, u= 0.559, us= 0.615, err= -0.5589385E-01 xg= 0.200, yg=-0.600, u= 0.465, us= 0.592, err= -0.1273269E+00 xg= 0.200, yg=-0.400, u= 0.352, us= 0.575, err= -0.2231016E+00 xg= 0.200, yg=-0.200, u= 0.204, us= 0.563, err= -0.3593701E+00 xg= 0.200, yg= 0.000, u= 0.000, us= 0.559, err= -0.5586741E+00 xg= 0.200, yg= 0.200, u= 0.204, us= 0.563, err= -0.3593701E+00 xg= 0.200, yg= 0.400, u= 0.352, us= 0.575, err= -0.2231016E+00 xg= 0.200, yg= 0.600, u= 0.465, us= 0.592, err= -0.1273269E+00 xg= 0.200, yg= 0.800, u= 0.559, us= 0.615, err= -0.5589385E-01 xg= 0.400, yg=-0.800, u= 0.497, us= 0.534, err= -0.3689889E-01 xg= 0.400, yg=-0.600, u= 0.401, us= 0.506, err= -0.1050118E+00 xg= 0.400, yg=-0.400, u= 0.288, us= 0.483, err= -0.1955376E+00 xg= 0.400, yg=-0.200, u= 0.154, us= 0.467, err= -0.3133461E+00 xg= 0.400, yg= 0.000, u= 0.000, us= 0.461, err= -0.4607336E+00 xg= 0.400, yg= 0.200, u= 0.154, us= 0.467, err= -0.3133461E+00 xg= 0.400, yg= 0.400, u= 0.288, us= 0.483, err= -0.1955376E+00 xg= 0.400, yg= 0.600, u= 0.401, us= 0.506, err= -0.1050118E+00 xg= 0.400, yg= 0.800, u= 0.497, us= 0.534, err= -0.3689889E-01 xg= 0.600, yg=-0.800, u= 0.447, us= 0.437, err= 0.9941831E-02 xg= 0.600, yg=-0.600, u= 0.353, us= 0.415, err= -0.6246559E-01 xg= 0.600, yg=-0.400, u= 0.246, us= 0.387, err= -0.1406883E+00 xg= 0.600, yg=-0.200, u= 0.127, us= 0.361, err= -0.2332222E+00 xg= 0.600, yg= 0.000, u= 0.000, us= 0.349, err= -0.3492635E+00 xg= 0.600, yg= 0.200, u= 0.127, us= 0.361, err= -0.2332222E+00 xg= 0.600, yg= 0.400, u= 0.246, us= 0.387, err= -0.1406883E+00 xg= 0.600, yg= 0.600, u= 0.353, us= 0.415, err= -0.6246559E-01 xg= 0.600, yg= 0.800, u= 0.447, us= 0.437, err= 0.9941831E-02 xg= 0.800, yg=-0.800, u= 0.407, us= 0.324, err= 0.8334436E-01 xg= 0.800, yg=-0.600, u= 0.316, us= 0.334, err= -0.1778155E-01 xg= 0.800, yg=-0.400, u= 0.217, us= 0.289, err= -0.7163264E-01 xg= 0.800, yg=-0.200, u= 0.111, us= 0.239, err= -0.1280829E+00 xg= 0.800, yg= 0.000, u= 0.000, us= 0.211, err= -0.2111930E+00 xg= 0.800, yg= 0.200, u= 0.111, us= 0.239, err= -0.1280829E+00 xg= 0.800, yg= 0.400, u= 0.217, us= 0.289, err= -0.7163264E-01 xg= 0.800, yg= 0.600, u= 0.316, us= 0.334, err= -0.1778155E-01 xg= 0.800, yg= 0.800, u= 0.407, us= 0.324, err= 0.8334436E-01 avgerr= 0.13989358E+00 maxerr= 0.64782065E+00 writing corner0_f90.dat finished writing corner0_f90.dat corner0.f90 finished in 0.598 seconds