corner0c.c running differential equation to solve d^2u/dx^2 + d^2u/dy^2 = c(x,y) = 0 uniform grid on rectangle 0.01,1 to 0.01,1 known Solution, for testing method alpha = Pi/omega omega=2Pi r = sqrt(x^2+y^2) theta = atan2(y,x) u(x,y) = r^alpha * sin(alpha*theta) xg( 0)=0.010000 xg( 1)=0.109000 xg( 2)=0.208000 xg( 3)=0.307000 xg( 4)=0.406000 xg( 5)=0.505000 xg( 6)=0.604000 xg( 7)=0.703000 xg( 8)=0.802000 xg( 9)=0.901000 xg(10)=1.000000 yg( 0)=0.010000 yg( 1)=0.109000 yg( 2)=0.208000 yg( 3)=0.307000 yg( 4)=0.406000 yg( 5)=0.505000 yg( 6)=0.604000 yg( 7)=0.703000 yg( 8)=0.802000 yg( 9)=0.901000 yg(10)=1.000000 xmin=0.010000, xmax=1.000000, hx=0.099000, nx=11 ymin=0.010000, ymax=1.000000, hy=0.099000, ny=11 x= 1.0000, y= 0.0000, th= 0.0000, U= 0.0000 x= 1.0000, y= 1.0000, th= 0.7854, U= 0.4551 x= 0.0000, y= 1.0000, th= 1.5708, U= 0.7071 x=-1.0000, y= 1.0000, th= 2.3562, U= 1.0987 x=-1.0000, y= 0.0000, th= 3.1416, U= 1.0000 x=-1.0000, y=-1.0000, th= 3.9270, U= 1.0987 x= 0.0000, y=-1.0000, th= 4.7124, U= 0.7071 x= 1.0000, y=-1.0000, th= 5.4978, U= 0.4551 x= 0.0000, y= 0.0000, th= 0.0000, U= 0.0000 internal cells zeroed matrix initialized row i= 1, j= 1, is bad err=0.0115394 row i= 1, j= 2, is bad err=-0.0199855 row i= 1, j= 3, is bad err=0.00919614 row i= 1, j= 7, is bad err=-0.00102805 row i= 1, j= 8, is bad err=0.00405334 row i= 1, j= 9, is bad err=-0.0256122 row i= 2, j= 1, is bad err=-0.00550709 row i= 2, j= 2, is bad err=0.00278308 row i= 2, j= 9, is bad err=-0.00125278 row i= 3, j= 1, is bad err=-0.00706403 row i= 3, j= 9, is bad err=0.00194287 row i= 8, j= 1, is bad err=-0.00153387 row i= 9, j= 1, is bad err=0.00950612 row i= 9, j= 2, is bad err=0.00598412 check_soln against PDE check soln against PDE max error=2.22165e-11 exact solution u, computed us, error xg[ 0]=0.01000, yg[ 0]=0.01000, u= 4.550899e-02, us= 4.550899e-02, err= 0.000000e+00 xg[ 0]=0.01000, yg[ 1]=0.10900, u= 2.229997e-01, us= 2.229997e-01, err= 0.000000e+00 xg[ 0]=0.01000, yg[ 2]=0.20800, u= 3.148335e-01, us= 3.148335e-01, err= 0.000000e+00 xg[ 0]=0.01000, yg[ 3]=0.30700, u= 3.854626e-01, us= 3.854626e-01, err= 0.000000e+00 xg[ 0]=0.01000, yg[ 4]=0.40600, u= 4.450411e-01, us= 4.450411e-01, err= 0.000000e+00 xg[ 0]=0.01000, yg[ 5]=0.50500, u= 4.975435e-01, us= 4.975435e-01, err= 0.000000e+00 xg[ 0]=0.01000, yg[ 6]=0.60400, u= 5.450150e-01, us= 5.450150e-01, err= 0.000000e+00 xg[ 0]=0.01000, yg[ 7]=0.70300, u= 5.886727e-01, us= 5.886727e-01, err= 0.000000e+00 xg[ 0]=0.01000, yg[ 8]=0.80200, u= 6.293101e-01, us= 6.293101e-01, err= 0.000000e+00 xg[ 0]=0.01000, yg[ 9]=0.90100, u= 6.674786e-01, us= 6.674786e-01, err= 0.000000e+00 xg[ 0]=0.01000, yg[10]=1.00000, u= 7.035801e-01, us= 7.035801e-01, err= 0.000000e+00 xg[ 1]=0.10900, yg[ 0]=0.01000, u= 1.512869e-02, us= 1.512869e-02, err= 0.000000e+00 xg[ 1]=0.10900, yg[ 1]=0.10900, u= 1.502486e-01, us= 1.505869e-01, err= 3.383495e-04 xg[ 1]=0.10900, yg[ 2]=0.20800, u= 2.508284e-01, us= 2.508397e-01, err= 1.131865e-05 xg[ 1]=0.10900, yg[ 3]=0.30700, u= 3.292233e-01, us= 3.292571e-01, err= 3.374819e-05 xg[ 1]=0.10900, yg[ 4]=0.40600, u= 3.945740e-01, us= 3.945961e-01, err= 2.213274e-05 xg[ 1]=0.10900, yg[ 5]=0.50500, u= 4.514584e-01, us= 4.514677e-01, err= 9.287642e-06 xg[ 1]=0.10900, yg[ 6]=0.60400, u= 5.023726e-01, us= 5.023753e-01, err= 2.734555e-06 xg[ 1]=0.10900, yg[ 7]=0.70300, u= 5.488169e-01, us= 5.488155e-01, err= 1.405192e-06 xg[ 1]=0.10900, yg[ 8]=0.80200, u= 5.917657e-01, us= 5.917586e-01, err= 7.034649e-06 xg[ 1]=0.10900, yg[ 9]=0.90100, u= 6.318897e-01, us= 6.318524e-01, err= 3.736152e-05 xg[ 1]=0.10900, yg[10]=1.00000, u= 6.696727e-01, us= 6.696727e-01, err= 0.000000e+00 xg[ 2]=0.20800, yg[ 0]=0.01000, u= 1.096006e-02, us= 1.096006e-02, err= 0.000000e+00 xg[ 2]=0.20800, yg[ 1]=0.10900, u= 1.158225e-01, us= 1.159476e-01, err= 1.250345e-04 xg[ 2]=0.20800, yg[ 2]=0.20800, u= 2.075529e-01, us= 2.076141e-01, err= 6.114117e-05 xg[ 2]=0.20800, yg[ 3]=0.30700, u= 2.853309e-01, us= 2.853627e-01, err= 3.175998e-05 xg[ 2]=0.20800, yg[ 4]=0.40600, u= 3.522640e-01, us= 3.522841e-01, err= 2.014935e-05 xg[ 2]=0.20800, yg[ 5]=0.50500, u= 4.111924e-01, us= 4.112038e-01, err= 1.135014e-05 xg[ 2]=0.20800, yg[ 6]=0.60400, u= 4.641182e-01, us= 4.641229e-01, err= 4.748875e-06 xg[ 2]=0.20800, yg[ 7]=0.70300, u= 5.124088e-01, us= 5.124078e-01, err= 9.670008e-07 xg[ 2]=0.20800, yg[ 8]=0.80200, u= 5.570160e-01, us= 5.570075e-01, err= 8.480977e-06 xg[ 2]=0.20800, yg[ 9]=0.90100, u= 5.986223e-01, us= 5.985987e-01, err= 2.357467e-05 xg[ 2]=0.20800, yg[10]=1.00000, u= 6.377315e-01, us= 6.377315e-01, err= 0.000000e+00 xg[ 3]=0.30700, yg[ 0]=0.01000, u= 9.022840e-03, us= 9.022840e-03, err= 0.000000e+00 xg[ 3]=0.30700, yg[ 1]=0.10900, u= 9.689168e-02, us= 9.690202e-02, err= 1.033809e-05 xg[ 3]=0.30700, yg[ 2]=0.20800, u= 1.786441e-01, us= 1.786756e-01, err= 3.144279e-05 xg[ 3]=0.30700, yg[ 3]=0.30700, u= 2.521543e-01, us= 2.521789e-01, err= 2.463156e-05 xg[ 3]=0.30700, yg[ 4]=0.40600, u= 3.178081e-01, us= 3.178253e-01, err= 1.719133e-05 xg[ 3]=0.30700, yg[ 5]=0.50500, u= 3.768249e-01, us= 3.768358e-01, err= 1.082890e-05 xg[ 3]=0.30700, yg[ 6]=0.60400, u= 4.304320e-01, us= 4.304375e-01, err= 5.549483e-06 xg[ 3]=0.30700, yg[ 7]=0.70300, u= 4.796406e-01, us= 4.796416e-01, err= 1.064761e-06 xg[ 3]=0.30700, yg[ 8]=0.80200, u= 5.252384e-01, us= 5.252356e-01, err= 2.829732e-06 xg[ 3]=0.30700, yg[ 9]=0.90100, u= 5.678321e-01, us= 5.678301e-01, err= 2.026594e-06 xg[ 3]=0.30700, yg[10]=1.00000, u= 6.078913e-01, us= 6.078913e-01, err= 0.000000e+00 xg[ 4]=0.40600, yg[ 0]=0.01000, u= 7.846465e-03, us= 7.846465e-03, err= 0.000000e+00 xg[ 4]=0.40600, yg[ 1]=0.10900, u= 8.478565e-02, us= 8.478979e-02, err= 4.144960e-06 xg[ 4]=0.40600, yg[ 2]=0.20800, u= 1.583979e-01, us= 1.584127e-01, err= 1.482379e-05 xg[ 4]=0.40600, yg[ 3]=0.30700, u= 2.269404e-01, us= 2.269563e-01, err= 1.583283e-05 xg[ 4]=0.40600, yg[ 4]=0.40600, u= 2.899747e-01, us= 2.899877e-01, err= 1.295776e-05 xg[ 4]=0.40600, yg[ 5]=0.50500, u= 3.478267e-01, us= 3.478359e-01, err= 9.190986e-06 xg[ 4]=0.40600, yg[ 6]=0.60400, u= 4.011059e-01, us= 4.011115e-01, err= 5.598777e-06 xg[ 4]=0.40600, yg[ 7]=0.70300, u= 4.504530e-01, us= 4.504557e-01, err= 2.661033e-06 xg[ 4]=0.40600, yg[ 8]=0.80200, u= 4.964426e-01, us= 4.964436e-01, err= 1.011439e-06 xg[ 4]=0.40600, yg[ 9]=0.90100, u= 5.395598e-01, us= 5.395625e-01, err= 2.775227e-06 xg[ 4]=0.40600, yg[10]=1.00000, u= 5.802050e-01, us= 5.802050e-01, err= 0.000000e+00 xg[ 5]=0.50500, yg[ 0]=0.01000, u= 7.035631e-03, us= 7.035631e-03, err= 0.000000e+00 xg[ 5]=0.50500, yg[ 1]=0.10900, u= 7.625438e-02, us= 7.625994e-02, err= 5.557833e-06 xg[ 5]=0.50500, yg[ 2]=0.20800, u= 1.434545e-01, us= 1.434634e-01, err= 8.855434e-06 xg[ 5]=0.50500, yg[ 3]=0.30700, u= 2.073573e-01, us= 2.073675e-01, err= 1.026702e-05 xg[ 5]=0.50500, yg[ 4]=0.40600, u= 2.673638e-01, us= 2.673732e-01, err= 9.341887e-06 xg[ 5]=0.50500, yg[ 5]=0.50500, u= 3.234021e-01, us= 3.234094e-01, err= 7.295750e-06 xg[ 5]=0.50500, yg[ 6]=0.60400, u= 3.756992e-01, us= 3.757043e-01, err= 5.031725e-06 xg[ 5]=0.50500, yg[ 7]=0.70300, u= 4.246075e-01, us= 4.246106e-01, err= 3.115400e-06 xg[ 5]=0.50500, yg[ 8]=0.80200, u= 4.705047e-01, us= 4.705067e-01, err= 1.975629e-06 xg[ 5]=0.50500, yg[ 9]=0.90100, u= 5.137474e-01, us= 5.137491e-01, err= 1.784537e-06 xg[ 5]=0.50500, yg[10]=1.00000, u= 5.546526e-01, us= 5.546526e-01, err= 0.000000e+00 xg[ 6]=0.60400, yg[ 0]=0.01000, u= 6.433342e-03, us= 6.433342e-03, err= 0.000000e+00 xg[ 6]=0.60400, yg[ 1]=0.10900, u= 6.984435e-02, us= 6.984851e-02, err= 4.158480e-06 xg[ 6]=0.60400, yg[ 2]=0.20800, u= 1.319307e-01, us= 1.319367e-01, err= 6.020432e-06 xg[ 6]=0.60400, yg[ 3]=0.30700, u= 1.917594e-01, us= 1.917665e-01, err= 7.113258e-06 xg[ 6]=0.60400, yg[ 4]=0.40600, u= 2.487689e-01, us= 2.487757e-01, err= 6.766658e-06 xg[ 6]=0.60400, yg[ 5]=0.50500, u= 3.027374e-01, us= 3.027429e-01, err= 5.556317e-06 xg[ 6]=0.60400, yg[ 6]=0.60400, u= 3.536842e-01, us= 3.536883e-01, err= 4.102895e-06 xg[ 6]=0.60400, yg[ 7]=0.70300, u= 4.017686e-01, us= 4.017714e-01, err= 2.782466e-06 xg[ 6]=0.60400, yg[ 8]=0.80200, u= 4.472147e-01, us= 4.472165e-01, err= 1.762265e-06 xg[ 6]=0.60400, yg[ 9]=0.90100, u= 4.902651e-01, us= 4.902660e-01, err= 8.660173e-07 xg[ 6]=0.60400, yg[10]=1.00000, u= 5.311560e-01, us= 5.311560e-01, err= 0.000000e+00 xg[ 7]=0.70300, yg[ 0]=0.01000, u= 5.963227e-03, us= 5.963227e-03, err= 0.000000e+00 xg[ 7]=0.70300, yg[ 1]=0.10900, u= 6.480752e-02, us= 6.480924e-02, err= 1.726760e-06 xg[ 7]=0.70300, yg[ 2]=0.20800, u= 1.227304e-01, us= 1.227349e-01, err= 4.496911e-06 xg[ 7]=0.70300, yg[ 3]=0.30700, u= 1.790393e-01, us= 1.790449e-01, err= 5.551160e-06 xg[ 7]=0.70300, yg[ 4]=0.40600, u= 2.332551e-01, us= 2.332601e-01, err= 5.026864e-06 xg[ 7]=0.70300, yg[ 5]=0.50500, u= 2.851167e-01, us= 2.851207e-01, err= 4.007482e-06 xg[ 7]=0.70300, yg[ 6]=0.60400, u= 3.345415e-01, us= 3.345445e-01, err= 3.009016e-06 xg[ 7]=0.70300, yg[ 7]=0.70300, u= 3.815705e-01, us= 3.815726e-01, err= 2.113627e-06 xg[ 7]=0.70300, yg[ 8]=0.80200, u= 4.263189e-01, us= 4.263202e-01, err= 1.282834e-06 xg[ 7]=0.70300, yg[ 9]=0.90100, u= 4.689392e-01, us= 4.689397e-01, err= 4.870130e-07 xg[ 7]=0.70300, yg[10]=1.00000, u= 5.095971e-01, us= 5.095971e-01, err= 0.000000e+00 xg[ 8]=0.80200, yg[ 0]=0.01000, u= 5.583087e-03, us= 5.583087e-03, err= 0.000000e+00 xg[ 8]=0.80200, yg[ 1]=0.10900, u= 6.071744e-02, us= 6.071439e-02, err= 3.047598e-06 xg[ 8]=0.80200, yg[ 2]=0.20800, u= 1.151817e-01, us= 1.151867e-01, err= 5.015975e-06 xg[ 8]=0.80200, yg[ 3]=0.30700, u= 1.684500e-01, us= 1.684558e-01, err= 5.769289e-06 xg[ 8]=0.80200, yg[ 4]=0.40600, u= 2.201255e-01, us= 2.201292e-01, err= 3.688358e-06 xg[ 8]=0.80200, yg[ 5]=0.50500, u= 2.699532e-01, us= 2.699556e-01, err= 2.383466e-06 xg[ 8]=0.80200, yg[ 6]=0.60400, u= 3.178065e-01, us= 3.178083e-01, err= 1.799166e-06 xg[ 8]=0.80200, yg[ 7]=0.70300, u= 3.636589e-01, us= 3.636603e-01, err= 1.375145e-06 xg[ 8]=0.80200, yg[ 8]=0.80200, u= 4.075532e-01, us= 4.075540e-01, err= 8.123916e-07 xg[ 8]=0.80200, yg[ 9]=0.90100, u= 4.495753e-01, us= 4.495751e-01, err= 1.566374e-07 xg[ 8]=0.80200, yg[10]=1.00000, u= 4.898343e-01, us= 4.898343e-01, err= 0.000000e+00 xg[ 9]=0.90100, yg[ 0]=0.01000, u= 5.267456e-03, us= 5.267456e-03, err= 0.000000e+00 xg[ 9]=0.90100, yg[ 1]=0.10900, u= 5.731178e-02, us= 5.730534e-02, err= 6.444171e-06 xg[ 9]=0.90100, yg[ 2]=0.20800, u= 1.088514e-01, us= 1.088705e-01, err= 1.909096e-05 xg[ 9]=0.90100, yg[ 3]=0.30700, u= 1.594782e-01, us= 1.594855e-01, err= 7.351156e-06 xg[ 9]=0.90100, yg[ 4]=0.40600, u= 2.088653e-01, us= 2.088659e-01, err= 5.595840e-07 xg[ 9]=0.90100, yg[ 5]=0.50500, u= 2.567807e-01, us= 2.567807e-01, err= 2.576560e-08 xg[ 9]=0.90100, yg[ 6]=0.60400, u= 3.030840e-01, us= 3.030845e-01, err= 4.983929e-07 xg[ 9]=0.90100, yg[ 7]=0.70300, u= 3.477125e-01, us= 3.477132e-01, err= 7.244264e-07 xg[ 9]=0.90100, yg[ 8]=0.80200, u= 3.906635e-01, us= 3.906644e-01, err= 9.279684e-07 xg[ 9]=0.90100, yg[ 9]=0.90100, u= 4.319759e-01, us= 4.319754e-01, err= 5.194267e-07 xg[ 9]=0.90100, yg[10]=1.00000, u= 4.717158e-01, us= 4.717158e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 0]=0.01000, u= 4.999938e-03, us= 4.999938e-03, err= 0.000000e+00 xg[10]=1.00000, yg[ 1]=0.10900, u= 5.441948e-02, us= 5.441948e-02, err= 0.000000e+00 xg[10]=1.00000, yg[ 2]=0.20800, u= 1.034480e-01, us= 1.034480e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 3]=0.30700, u= 1.517623e-01, us= 1.517623e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 4]=0.40600, u= 1.990925e-01, us= 1.990925e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 5]=0.50500, u= 2.452335e-01, us= 2.452335e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 6]=0.60400, u= 2.900460e-01, us= 2.900460e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 7]=0.70300, u= 3.334505e-01, us= 3.334505e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 8]=0.80200, u= 3.754166e-01, us= 3.754166e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 9]=0.90100, u= 4.159517e-01, us= 4.159517e-01, err= 0.000000e+00 xg[10]=1.00000, yg[10]=1.00000, u= 4.550899e-01, us= 4.550899e-01, err= 0.000000e+00 avg_error= 1.365092e-05, max_error= 3.383495e-04 writing corner0c_c.dat finished writing corner0c_c.dat finished corner0c.c in 0.030000 seconds