pde_laplace.c running Laplace differential equation to solve d^2u/dx^2 + d^2u/dy^2 = c(x,y) = 0 uniform grid on rectangle 0,1 to 0,1 known Solution, for testing method u(x,y) = cos(kx)*cosh(kx) xg( 0)=0.000000 xg( 1)=0.062500 xg( 2)=0.125000 xg( 3)=0.187500 xg( 4)=0.250000 xg( 5)=0.312500 xg( 6)=0.375000 xg( 7)=0.437500 xg( 8)=0.500000 xg( 9)=0.562500 xg(10)=0.625000 xg(11)=0.687500 xg(12)=0.750000 xg(13)=0.812500 xg(14)=0.875000 xg(15)=0.937500 xg(16)=1.000000 yg( 0)=0.000000 yg( 1)=0.062500 yg( 2)=0.125000 yg( 3)=0.187500 yg( 4)=0.250000 yg( 5)=0.312500 yg( 6)=0.375000 yg( 7)=0.437500 yg( 8)=0.500000 yg( 9)=0.562500 yg(10)=0.625000 yg(11)=0.687500 yg(12)=0.750000 yg(13)=0.812500 yg(14)=0.875000 yg(15)=0.937500 yg(16)=1.000000 xmin=0.000000, xmax=1.000000, hx=0.062500, nx=17 ymin=0.000000, ymax=1.000000, hy=0.062500, ny=17 u(0.5,0.5)=-11.573560 k=6.280000 internal cells zeroed matrix initialized check_soln against PDE check soln against PDE max error=2.40892e-05 exact solution u, computed us, error xg[ 0]=0.00000, yg[ 0]=0.00000, u= 1.000000e+00, us= 1.000000e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 1]=0.06250, u= 1.078022e+00, us= 1.078022e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 2]=0.12500, u= 1.324263e+00, us= 1.324263e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 3]=0.18750, u= 1.777148e+00, us= 1.777148e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 4]=0.25000, u= 2.507347e+00, us= 2.507347e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 5]=0.31250, u= 3.628802e+00, us= 3.628802e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 6]=0.37500, u= 5.316511e+00, us= 5.316511e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 7]=0.43750, u= 7.833831e+00, us= 7.833831e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 8]=0.50000, u= 1.157357e+01, us= 1.157357e+01, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 9]=0.56250, u= 1.711931e+01, us= 1.711931e+01, err= 0.000000e+00 xg[ 0]=0.00000, yg[10]=0.62500, u= 2.533641e+01, us= 2.533641e+01, err= 0.000000e+00 xg[ 0]=0.00000, yg[11]=0.68750, u= 3.750711e+01, us= 3.750711e+01, err= 0.000000e+00 xg[ 0]=0.00000, yg[12]=0.75000, u= 5.553058e+01, us= 5.553058e+01, err= 0.000000e+00 xg[ 0]=0.00000, yg[13]=0.81250, u= 8.221928e+01, us= 8.221928e+01, err= 0.000000e+00 xg[ 0]=0.00000, yg[14]=0.87500, u= 1.217378e+02, us= 1.217378e+02, err= 0.000000e+00 xg[ 0]=0.00000, yg[15]=0.93750, u= 1.802528e+02, us= 1.802528e+02, err= 0.000000e+00 xg[ 0]=0.00000, yg[16]=1.00000, u= 2.668953e+02, us= 2.668953e+02, err= 0.000000e+00 xg[ 1]=0.06250, yg[ 0]=0.00000, u= 9.239557e-01, us= 9.239557e-01, err= 0.000000e+00 xg[ 1]=0.06250, yg[ 1]=0.06250, u= 9.960447e-01, us= 9.960447e-01, err= 1.877252e-08 xg[ 1]=0.06250, yg[ 2]=0.12500, u= 1.223561e+00, us= 1.223561e+00, err= 3.787617e-09 xg[ 1]=0.06250, yg[ 3]=0.18750, u= 1.642006e+00, us= 1.642006e+00, err= 6.811543e-10 xg[ 1]=0.06250, yg[ 4]=0.25000, u= 2.316677e+00, us= 2.316677e+00, err= 3.928618e-09 xg[ 1]=0.06250, yg[ 5]=0.31250, u= 3.352852e+00, us= 3.352852e+00, err= 6.067454e-09 xg[ 1]=0.06250, yg[ 6]=0.37500, u= 4.912221e+00, us= 4.912221e+00, err= 8.429066e-09 xg[ 1]=0.06250, yg[ 7]=0.43750, u= 7.238113e+00, us= 7.238113e+00, err= 1.133485e-08 xg[ 1]=0.06250, yg[ 8]=0.50000, u= 1.069347e+01, us= 1.069347e+01, err= 1.540000e-08 xg[ 1]=0.06250, yg[ 9]=0.56250, u= 1.581748e+01, us= 1.581748e+01, err= 2.107795e-08 xg[ 1]=0.06250, yg[10]=0.62500, u= 2.340972e+01, us= 2.340972e+01, err= 2.911630e-08 xg[ 1]=0.06250, yg[11]=0.68750, u= 3.465491e+01, us= 3.465491e+01, err= 4.032142e-08 xg[ 1]=0.06250, yg[12]=0.75000, u= 5.130780e+01, us= 5.130780e+01, err= 5.545147e-08 xg[ 1]=0.06250, yg[13]=0.81250, u= 7.596697e+01, us= 7.596697e+01, err= 7.487605e-08 xg[ 1]=0.06250, yg[14]=0.87500, u= 1.124803e+02, us= 1.124803e+02, err= 9.468869e-08 xg[ 1]=0.06250, yg[15]=0.93750, u= 1.665456e+02, us= 1.665456e+02, err= 9.938408e-08 xg[ 1]=0.06250, yg[16]=1.00000, u= 2.465994e+02, us= 2.465994e+02, err= 0.000000e+00 xg[ 2]=0.12500, yg[ 0]=0.00000, u= 7.073883e-01, us= 7.073883e-01, err= 0.000000e+00 xg[ 2]=0.12500, yg[ 1]=0.06250, u= 7.625802e-01, us= 7.625802e-01, err= 2.217839e-08 xg[ 2]=0.12500, yg[ 2]=0.12500, u= 9.367683e-01, us= 9.367683e-01, err= 5.911788e-09 xg[ 2]=0.12500, yg[ 3]=0.18750, u= 1.257134e+00, us= 1.257134e+00, err= 9.929225e-10 xg[ 2]=0.12500, yg[ 4]=0.25000, u= 1.773668e+00, us= 1.773668e+00, err= 4.805113e-09 xg[ 2]=0.12500, yg[ 5]=0.31250, u= 2.566972e+00, us= 2.566972e+00, err= 7.512607e-09 xg[ 2]=0.12500, yg[ 6]=0.37500, u= 3.760838e+00, us= 3.760838e+00, err= 9.790388e-09 xg[ 2]=0.12500, yg[ 7]=0.43750, u= 5.541560e+00, us= 5.541560e+00, err= 1.235464e-08 xg[ 2]=0.12500, yg[ 8]=0.50000, u= 8.187011e+00, us= 8.187011e+00, err= 1.570391e-08 xg[ 2]=0.12500, yg[ 9]=0.56250, u= 1.211000e+01, us= 1.211000e+01, err= 2.007277e-08 xg[ 2]=0.12500, yg[10]=0.62500, u= 1.792268e+01, us= 1.792268e+01, err= 2.594707e-08 xg[ 2]=0.12500, yg[11]=0.68750, u= 2.653209e+01, us= 2.653209e+01, err= 3.345002e-08 xg[ 2]=0.12500, yg[12]=0.75000, u= 3.928168e+01, us= 3.928168e+01, err= 4.256100e-08 xg[ 2]=0.12500, yg[13]=0.81250, u= 5.816095e+01, us= 5.816095e+01, err= 5.257496e-08 xg[ 2]=0.12500, yg[14]=0.87500, u= 8.611590e+01, us= 8.611590e+01, err= 6.073498e-08 xg[ 2]=0.12500, yg[15]=0.93750, u= 1.275087e+02, us= 1.275087e+02, err= 6.568415e-08 xg[ 2]=0.12500, yg[16]=1.00000, u= 1.887986e+02, us= 1.887986e+02, err= 0.000000e+00 xg[ 3]=0.18750, yg[ 0]=0.00000, u= 3.832351e-01, us= 3.832351e-01, err= 0.000000e+00 xg[ 3]=0.18750, yg[ 1]=0.06250, u= 4.131360e-01, us= 4.131359e-01, err= 1.172685e-08 xg[ 3]=0.18750, yg[ 2]=0.12500, u= 5.075042e-01, us= 5.075042e-01, err= 1.331148e-09 xg[ 3]=0.18750, yg[ 3]=0.18750, u= 6.810656e-01, us= 6.810656e-01, err= 3.988761e-09 xg[ 3]=0.18750, yg[ 4]=0.25000, u= 9.609034e-01, us= 9.609034e-01, err= 7.230389e-09 xg[ 3]=0.18750, yg[ 5]=0.31250, u= 1.390685e+00, us= 1.390685e+00, err= 9.260673e-09 xg[ 3]=0.18750, yg[ 6]=0.37500, u= 2.037474e+00, us= 2.037474e+00, err= 1.103665e-08 xg[ 3]=0.18750, yg[ 7]=0.43750, u= 3.002199e+00, us= 3.002199e+00, err= 1.291692e-08 xg[ 3]=0.18750, yg[ 8]=0.50000, u= 4.435401e+00, us= 4.435401e+00, err= 1.518798e-08 xg[ 3]=0.18750, yg[ 9]=0.56250, u= 6.560721e+00, us= 6.560721e+00, err= 1.802869e-08 xg[ 3]=0.18750, yg[10]=0.62500, u= 9.709803e+00, us= 9.709803e+00, err= 2.153338e-08 xg[ 3]=0.18750, yg[11]=0.68750, u= 1.437404e+01, us= 1.437404e+01, err= 2.566103e-08 xg[ 3]=0.18750, yg[12]=0.75000, u= 2.128127e+01, us= 2.128127e+01, err= 3.000465e-08 xg[ 3]=0.18750, yg[13]=0.81250, u= 3.150932e+01, us= 3.150932e+01, err= 3.362156e-08 xg[ 3]=0.18750, yg[14]=0.87500, u= 4.665421e+01, us= 4.665421e+01, err= 3.558895e-08 xg[ 3]=0.18750, yg[15]=0.93750, u= 6.907922e+01, us= 6.907922e+01, err= 3.695198e-08 xg[ 3]=0.18750, yg[16]=1.00000, u= 1.022836e+02, us= 1.022836e+02, err= 0.000000e+00 xg[ 4]=0.25000, yg[ 0]=0.00000, u= 7.963267e-04, us= 7.963267e-04, err= 0.000000e+00 xg[ 4]=0.25000, yg[ 1]=0.06250, u= 8.584578e-04, us= 8.584620e-04, err= 4.186291e-09 xg[ 4]=0.25000, yg[ 2]=0.12500, u= 1.054546e-03, us= 1.054554e-03, err= 7.254955e-09 xg[ 4]=0.25000, yg[ 3]=0.18750, u= 1.415191e-03, us= 1.415200e-03, err= 9.404168e-09 xg[ 4]=0.25000, yg[ 4]=0.25000, u= 1.996667e-03, us= 1.996678e-03, err= 1.051132e-08 xg[ 4]=0.25000, yg[ 5]=0.31250, u= 2.889712e-03, us= 2.889723e-03, err= 1.136411e-08 xg[ 4]=0.25000, yg[ 6]=0.37500, u= 4.233680e-03, us= 4.233692e-03, err= 1.214766e-08 xg[ 4]=0.25000, yg[ 7]=0.43750, u= 6.238289e-03, us= 6.238302e-03, err= 1.302240e-08 xg[ 4]=0.25000, yg[ 8]=0.50000, u= 9.216347e-03, us= 9.216361e-03, err= 1.403994e-08 xg[ 4]=0.25000, yg[ 9]=0.56250, u= 1.363256e-02, us= 1.363258e-02, err= 1.526701e-08 xg[ 4]=0.25000, yg[10]=0.62500, u= 2.017606e-02, us= 2.017608e-02, err= 1.648747e-08 xg[ 4]=0.25000, yg[11]=0.68750, u= 2.986792e-02, us= 2.986793e-02, err= 1.745215e-08 xg[ 4]=0.25000, yg[12]=0.75000, u= 4.422049e-02, us= 4.422050e-02, err= 1.769728e-08 xg[ 4]=0.25000, yg[13]=0.81250, u= 6.547341e-02, us= 6.547342e-02, err= 1.638562e-08 xg[ 4]=0.25000, yg[14]=0.87500, u= 9.694308e-02, us= 9.694309e-02, err= 1.294378e-08 xg[ 4]=0.25000, yg[15]=0.93750, u= 1.435401e-01, us= 1.435402e-01, err= 7.428967e-09 xg[ 4]=0.25000, yg[16]=1.00000, u= 2.125358e-01, us= 2.125358e-01, err= 0.000000e+00 xg[ 5]=0.31250, yg[ 0]=0.00000, u= -3.817636e-01, us= -3.817636e-01, err= 0.000000e+00 xg[ 5]=0.31250, yg[ 1]=0.06250, u= -4.115496e-01, us= -4.115496e-01, err= 2.093051e-08 xg[ 5]=0.31250, yg[ 2]=0.12500, u= -5.055555e-01, us= -5.055555e-01, err= 1.713189e-08 xg[ 5]=0.31250, yg[ 3]=0.18750, u= -6.784505e-01, us= -6.784505e-01, err= 1.542339e-08 xg[ 5]=0.31250, yg[ 4]=0.25000, u= -9.572137e-01, us= -9.572137e-01, err= 1.423943e-08 xg[ 5]=0.31250, yg[ 5]=0.31250, u= -1.385345e+00, us= -1.385345e+00, err= 1.355700e-08 xg[ 5]=0.31250, yg[ 6]=0.37500, u= -2.029650e+00, us= -2.029650e+00, err= 1.312761e-08 xg[ 5]=0.31250, yg[ 7]=0.43750, u= -2.990672e+00, us= -2.990672e+00, err= 1.289059e-08 xg[ 5]=0.31250, yg[ 8]=0.50000, u= -4.418370e+00, us= -4.418370e+00, err= 1.273012e-08 xg[ 5]=0.31250, yg[ 9]=0.56250, u= -6.535529e+00, us= -6.535529e+00, err= 1.243128e-08 xg[ 5]=0.31250, yg[10]=0.62500, u= -9.672519e+00, us= -9.672519e+00, err= 1.166419e-08 xg[ 5]=0.31250, yg[11]=0.68750, u= -1.431885e+01, us= -1.431885e+01, err= 9.994178e-09 xg[ 5]=0.31250, yg[12]=0.75000, u= -2.119956e+01, us= -2.119956e+01, err= 6.802680e-09 xg[ 5]=0.31250, yg[13]=0.81250, u= -3.138833e+01, us= -3.138833e+01, err= 1.341485e-09 xg[ 5]=0.31250, yg[14]=0.87500, u= -4.647507e+01, us= -4.647507e+01, err= 7.219511e-09 xg[ 5]=0.31250, yg[15]=0.93750, u= -6.881397e+01, us= -6.881397e+01, err= 2.050704e-08 xg[ 5]=0.31250, yg[16]=1.00000, u= -1.018909e+02, us= -1.018909e+02, err= 0.000000e+00 xg[ 6]=0.37500, yg[ 0]=0.00000, u= -7.062616e-01, us= -7.062616e-01, err= 0.000000e+00 xg[ 6]=0.37500, yg[ 1]=0.06250, u= -7.613657e-01, us= -7.613656e-01, err= 3.502263e-08 xg[ 6]=0.37500, yg[ 2]=0.12500, u= -9.352764e-01, us= -9.352764e-01, err= 2.593340e-08 xg[ 6]=0.37500, yg[ 3]=0.18750, u= -1.255132e+00, us= -1.255132e+00, err= 2.090310e-08 xg[ 6]=0.37500, yg[ 4]=0.25000, u= -1.770843e+00, us= -1.770843e+00, err= 1.757635e-08 xg[ 6]=0.37500, yg[ 5]=0.31250, u= -2.562884e+00, us= -2.562884e+00, err= 1.540567e-08 xg[ 6]=0.37500, yg[ 6]=0.37500, u= -3.754848e+00, us= -3.754848e+00, err= 1.391100e-08 xg[ 6]=0.37500, yg[ 7]=0.43750, u= -5.532734e+00, us= -5.532734e+00, err= 1.273459e-08 xg[ 6]=0.37500, yg[ 8]=0.50000, u= -8.173972e+00, us= -8.173972e+00, err= 1.154059e-08 xg[ 6]=0.37500, yg[ 9]=0.56250, u= -1.209071e+01, us= -1.209071e+01, err= 1.002576e-08 xg[ 6]=0.37500, yg[10]=0.62500, u= -1.789413e+01, us= -1.789413e+01, err= 7.716402e-09 xg[ 6]=0.37500, yg[11]=0.68750, u= -2.648983e+01, us= -2.648983e+01, err= 4.053226e-09 xg[ 6]=0.37500, yg[12]=0.75000, u= -3.921912e+01, us= -3.921912e+01, err= 1.715083e-09 xg[ 6]=0.37500, yg[13]=0.81250, u= -5.806832e+01, us= -5.806832e+01, err= 1.057853e-08 xg[ 6]=0.37500, yg[14]=0.87500, u= -8.597875e+01, us= -8.597875e+01, err= 2.354665e-08 xg[ 6]=0.37500, yg[15]=0.93750, u= -1.273057e+02, us= -1.273057e+02, err= 4.344756e-08 xg[ 6]=0.37500, yg[16]=1.00000, u= -1.884979e+02, us= -1.884979e+02, err= 0.000000e+00 xg[ 7]=0.43750, yg[ 0]=0.00000, u= -9.233453e-01, us= -9.233453e-01, err= 0.000000e+00 xg[ 7]=0.43750, yg[ 1]=0.06250, u= -9.953867e-01, us= -9.953866e-01, err= 4.466275e-08 xg[ 7]=0.43750, yg[ 2]=0.12500, u= -1.222752e+00, us= -1.222752e+00, err= 3.191261e-08 xg[ 7]=0.43750, yg[ 3]=0.18750, u= -1.640921e+00, us= -1.640921e+00, err= 2.465909e-08 xg[ 7]=0.43750, yg[ 4]=0.25000, u= -2.315147e+00, us= -2.315147e+00, err= 1.980469e-08 xg[ 7]=0.43750, yg[ 5]=0.31250, u= -3.350638e+00, us= -3.350638e+00, err= 1.663398e-08 xg[ 7]=0.43750, yg[ 6]=0.37500, u= -4.908976e+00, us= -4.908976e+00, err= 1.437541e-08 xg[ 7]=0.43750, yg[ 7]=0.43750, u= -7.233331e+00, us= -7.233331e+00, err= 1.254269e-08 xg[ 7]=0.43750, yg[ 8]=0.50000, u= -1.068641e+01, us= -1.068641e+01, err= 1.069153e-08 xg[ 7]=0.43750, yg[ 9]=0.56250, u= -1.580703e+01, us= -1.580703e+01, err= 8.382520e-09 xg[ 7]=0.43750, yg[10]=0.62500, u= -2.339426e+01, us= -2.339426e+01, err= 5.079526e-09 xg[ 7]=0.43750, yg[11]=0.68750, u= -3.463202e+01, us= -3.463202e+01, err= 1.384549e-10 xg[ 7]=0.43750, yg[12]=0.75000, u= -5.127390e+01, us= -5.127390e+01, err= 7.263120e-09 xg[ 7]=0.43750, yg[13]=0.81250, u= -7.591679e+01, us= -7.591679e+01, err= 1.829262e-08 xg[ 7]=0.43750, yg[14]=0.87500, u= -1.124060e+02, us= -1.124060e+02, err= 3.419194e-08 xg[ 7]=0.43750, yg[15]=0.93750, u= -1.664356e+02, us= -1.664356e+02, err= 5.892423e-08 xg[ 7]=0.43750, yg[16]=1.00000, u= -2.464365e+02, us= -2.464365e+02, err= 0.000000e+00 xg[ 8]=0.50000, yg[ 0]=0.00000, u= -9.999987e-01, us= -9.999987e-01, err= 0.000000e+00 xg[ 8]=0.50000, yg[ 1]=0.06250, u= -1.078021e+00, us= -1.078021e+00, err= 4.818395e-08 xg[ 8]=0.50000, yg[ 2]=0.12500, u= -1.324262e+00, us= -1.324262e+00, err= 3.396895e-08 xg[ 8]=0.50000, yg[ 3]=0.18750, u= -1.777146e+00, us= -1.777146e+00, err= 2.585572e-08 xg[ 8]=0.50000, yg[ 4]=0.25000, u= -2.507344e+00, us= -2.507343e+00, err= 2.049627e-08 xg[ 8]=0.50000, yg[ 5]=0.31250, u= -3.628798e+00, us= -3.628798e+00, err= 1.694667e-08 xg[ 8]=0.50000, yg[ 6]=0.37500, u= -5.316504e+00, us= -5.316504e+00, err= 1.443099e-08 xg[ 8]=0.50000, yg[ 7]=0.43750, u= -7.833821e+00, us= -7.833821e+00, err= 1.237580e-08 xg[ 8]=0.50000, yg[ 8]=0.50000, u= -1.157356e+01, us= -1.157356e+01, err= 1.030041e-08 xg[ 8]=0.50000, yg[ 9]=0.56250, u= -1.711929e+01, us= -1.711929e+01, err= 7.708575e-09 xg[ 8]=0.50000, yg[10]=0.62500, u= -2.533638e+01, us= -2.533638e+01, err= 4.059154e-09 xg[ 8]=0.50000, yg[11]=0.68750, u= -3.750706e+01, us= -3.750706e+01, err= 1.328075e-09 xg[ 8]=0.50000, yg[12]=0.75000, u= -5.553051e+01, us= -5.553051e+01, err= 9.315685e-09 xg[ 8]=0.50000, yg[13]=0.81250, u= -8.221917e+01, us= -8.221917e+01, err= 2.106089e-08 xg[ 8]=0.50000, yg[14]=0.87500, u= -1.217377e+02, us= -1.217377e+02, err= 3.790144e-08 xg[ 8]=0.50000, yg[15]=0.93750, u= -1.802526e+02, us= -1.802526e+02, err= 6.438714e-08 xg[ 8]=0.50000, yg[16]=1.00000, u= -2.668949e+02, us= -2.668949e+02, err= 0.000000e+00 xg[ 9]=0.56250, yg[ 0]=0.00000, u= -9.245637e-01, us= -9.245637e-01, err= 0.000000e+00 xg[ 9]=0.56250, yg[ 1]=0.06250, u= -9.967001e-01, us= -9.967001e-01, err= 4.471872e-08 xg[ 9]=0.56250, yg[ 2]=0.12500, u= -1.224366e+00, us= -1.224366e+00, err= 3.165057e-08 xg[ 9]=0.56250, yg[ 3]=0.18750, u= -1.643087e+00, us= -1.643087e+00, err= 2.426499e-08 xg[ 9]=0.56250, yg[ 4]=0.25000, u= -2.318202e+00, us= -2.318202e+00, err= 1.942044e-08 xg[ 9]=0.56250, yg[ 5]=0.31250, u= -3.355059e+00, us= -3.355059e+00, err= 1.625961e-08 xg[ 9]=0.56250, yg[ 6]=0.37500, u= -4.915453e+00, us= -4.915453e+00, err= 1.404519e-08 xg[ 9]=0.56250, yg[ 7]=0.43750, u= -7.242876e+00, us= -7.242876e+00, err= 1.223885e-08 xg[ 9]=0.56250, yg[ 8]=0.50000, u= -1.070051e+01, us= -1.070051e+01, err= 1.040263e-08 xg[ 9]=0.56250, yg[ 9]=0.56250, u= -1.582789e+01, us= -1.582789e+01, err= 8.075309e-09 xg[ 9]=0.56250, yg[10]=0.62500, u= -2.342513e+01, us= -2.342513e+01, err= 4.743721e-09 xg[ 9]=0.56250, yg[11]=0.68750, u= -3.467772e+01, us= -3.467772e+01, err= 2.325149e-10 xg[ 9]=0.56250, yg[12]=0.75000, u= -5.134156e+01, us= -5.134156e+01, err= 7.666483e-09 xg[ 9]=0.56250, yg[13]=0.81250, u= -7.601696e+01, us= -7.601696e+01, err= 1.867352e-08 xg[ 9]=0.56250, yg[14]=0.87500, u= -1.125544e+02, us= -1.125544e+02, err= 3.444044e-08 xg[ 9]=0.56250, yg[15]=0.93750, u= -1.666552e+02, us= -1.666552e+02, err= 5.916036e-08 xg[ 9]=0.56250, yg[16]=1.00000, u= -2.467617e+02, us= -2.467617e+02, err= 0.000000e+00 xg[10]=0.62500, yg[ 0]=0.00000, u= -7.085131e-01, us= -7.085131e-01, err= 0.000000e+00 xg[10]=0.62500, yg[ 1]=0.06250, u= -7.637928e-01, us= -7.637927e-01, err= 3.483173e-08 xg[10]=0.62500, yg[ 2]=0.12500, u= -9.382579e-01, us= -9.382579e-01, err= 2.527819e-08 xg[10]=0.62500, yg[ 3]=0.18750, u= -1.259133e+00, us= -1.259133e+00, err= 2.006678e-08 xg[10]=0.62500, yg[ 4]=0.25000, u= -1.776488e+00, us= -1.776488e+00, err= 1.674752e-08 xg[10]=0.62500, yg[ 5]=0.31250, u= -2.571054e+00, us= -2.571054e+00, err= 1.465965e-08 xg[10]=0.62500, yg[ 6]=0.37500, u= -3.766818e+00, us= -3.766818e+00, err= 1.324555e-08 xg[10]=0.62500, yg[ 7]=0.43750, u= -5.550372e+00, us= -5.550372e+00, err= 1.212913e-08 xg[10]=0.62500, yg[ 8]=0.50000, u= -8.200029e+00, us= -8.200029e+00, err= 1.097225e-08 xg[10]=0.62500, yg[ 9]=0.56250, u= -1.212925e+01, us= -1.212925e+01, err= 9.423126e-09 xg[10]=0.62500, yg[10]=0.62500, u= -1.795118e+01, us= -1.795118e+01, err= 7.048673e-09 xg[10]=0.62500, yg[11]=0.68750, u= -2.657428e+01, us= -2.657428e+01, err= 3.288117e-09 xg[10]=0.62500, yg[12]=0.75000, u= -3.934414e+01, us= -3.934414e+01, err= 2.553560e-09 xg[10]=0.62500, yg[13]=0.81250, u= -5.825344e+01, us= -5.825344e+01, err= 1.140537e-08 xg[10]=0.62500, yg[14]=0.87500, u= -8.625284e+01, us= -8.625284e+01, err= 2.421529e-08 xg[10]=0.62500, yg[15]=0.93750, u= -1.277115e+02, us= -1.277115e+02, err= 4.412778e-08 xg[10]=0.62500, yg[16]=1.00000, u= -1.890988e+02, us= -1.890988e+02, err= 0.000000e+00 xg[11]=0.68750, yg[ 0]=0.00000, u= -3.847057e-01, us= -3.847057e-01, err= 0.000000e+00 xg[11]=0.68750, yg[ 1]=0.06250, u= -4.147213e-01, us= -4.147212e-01, err= 1.994615e-08 xg[11]=0.68750, yg[ 2]=0.12500, u= -5.094517e-01, us= -5.094517e-01, err= 1.581268e-08 xg[11]=0.68750, yg[ 3]=0.18750, u= -6.836791e-01, us= -6.836790e-01, err= 1.392950e-08 xg[11]=0.68750, yg[ 4]=0.25000, u= -9.645906e-01, us= -9.645906e-01, err= 1.290665e-08 xg[11]=0.68750, yg[ 5]=0.31250, u= -1.396021e+00, us= -1.396021e+00, err= 1.240085e-08 xg[11]=0.68750, yg[ 6]=0.37500, u= -2.045292e+00, us= -2.045292e+00, err= 1.216620e-08 xg[11]=0.68750, yg[ 7]=0.43750, u= -3.013720e+00, us= -3.013720e+00, err= 1.205813e-08 xg[11]=0.68750, yg[ 8]=0.50000, u= -4.452420e+00, us= -4.452420e+00, err= 1.192929e-08 xg[11]=0.68750, yg[ 9]=0.56250, u= -6.585896e+00, us= -6.585896e+00, err= 1.157842e-08 xg[11]=0.68750, yg[10]=0.62500, u= -9.747062e+00, us= -9.747062e+00, err= 1.070402e-08 xg[11]=0.68750, yg[11]=0.68750, u= -1.442920e+01, us= -1.442920e+01, err= 8.873291e-09 xg[11]=0.68750, yg[12]=0.75000, u= -2.136293e+01, us= -2.136293e+01, err= 5.514168e-09 xg[11]=0.68750, yg[13]=0.81250, u= -3.163023e+01, us= -3.163023e+01, err= 8.475616e-11 xg[11]=0.68750, yg[14]=0.87500, u= -4.683323e+01, us= -4.683323e+01, err= 8.547360e-09 xg[11]=0.68750, yg[15]=0.93750, u= -6.934430e+01, us= -6.934430e+01, err= 2.151153e-08 xg[11]=0.68750, yg[16]=1.00000, u= -1.026761e+02, us= -1.026761e+02, err= 0.000000e+00 xg[12]=0.75000, yg[ 0]=0.00000, u= -2.388978e-03, us= -2.388978e-03, err= 0.000000e+00 xg[12]=0.75000, yg[ 1]=0.06250, u= -2.575371e-03, us= -2.575369e-03, err= 2.400665e-09 xg[12]=0.75000, yg[ 2]=0.12500, u= -3.163636e-03, us= -3.163631e-03, err= 4.775656e-09 xg[12]=0.75000, yg[ 3]=0.18750, u= -4.245568e-03, us= -4.245561e-03, err= 6.918864e-09 xg[12]=0.75000, yg[ 4]=0.25000, u= -5.989996e-03, us= -5.989988e-03, err= 8.596682e-09 xg[12]=0.75000, yg[ 5]=0.31250, u= -8.669129e-03, us= -8.669119e-03, err= 9.880424e-09 xg[12]=0.75000, yg[ 6]=0.37500, u= -1.270103e-02, us= -1.270102e-02, err= 1.095740e-08 xg[12]=0.75000, yg[ 7]=0.43750, u= -1.871485e-02, us= -1.871484e-02, err= 1.199803e-08 xg[12]=0.75000, yg[ 8]=0.50000, u= -2.764902e-02, us= -2.764900e-02, err= 1.309250e-08 xg[12]=0.75000, yg[ 9]=0.56250, u= -4.089765e-02, us= -4.089764e-02, err= 1.423346e-08 xg[12]=0.75000, yg[10]=0.62500, u= -6.052813e-02, us= -6.052811e-02, err= 1.528906e-08 xg[12]=0.75000, yg[11]=0.68750, u= -8.960367e-02, us= -8.960365e-02, err= 1.596733e-08 xg[12]=0.75000, yg[12]=0.75000, u= -1.326613e-01, us= -1.326613e-01, err= 1.579852e-08 xg[12]=0.75000, yg[13]=0.81250, u= -1.964201e-01, us= -1.964200e-01, err= 1.418796e-08 xg[12]=0.75000, yg[14]=0.87500, u= -2.908290e-01, us= -2.908290e-01, err= 1.071938e-08 xg[12]=0.75000, yg[15]=0.93750, u= -4.306201e-01, us= -4.306201e-01, err= 5.628494e-09 xg[12]=0.75000, yg[16]=1.00000, u= -6.376070e-01, us= -6.376070e-01, err= 0.000000e+00 xg[13]=0.81250, yg[ 0]=0.00000, u= 3.802911e-01, us= 3.802911e-01, err= 0.000000e+00 xg[13]=0.81250, yg[ 1]=0.06250, u= 4.099622e-01, us= 4.099622e-01, err= 1.540306e-08 xg[13]=0.81250, yg[ 2]=0.12500, u= 5.036055e-01, us= 5.036055e-01, err= 5.982886e-09 xg[13]=0.81250, yg[ 3]=0.18750, u= 6.758336e-01, us= 6.758336e-01, err= 4.284240e-10 xg[13]=0.81250, yg[ 4]=0.25000, u= 9.535216e-01, us= 9.535216e-01, err= 4.701635e-09 xg[13]=0.81250, yg[ 5]=0.31250, u= 1.380001e+00, us= 1.380001e+00, err= 7.560737e-09 xg[13]=0.81250, yg[ 6]=0.37500, u= 2.021822e+00, us= 2.021822e+00, err= 9.772940e-09 xg[13]=0.81250, yg[ 7]=0.43750, u= 2.979136e+00, us= 2.979136e+00, err= 1.186786e-08 xg[13]=0.81250, yg[ 8]=0.50000, u= 4.401327e+00, us= 4.401327e+00, err= 1.419276e-08 xg[13]=0.81250, yg[ 9]=0.56250, u= 6.510320e+00, us= 6.510320e+00, err= 1.695256e-08 xg[13]=0.81250, yg[10]=0.62500, u= 9.635211e+00, us= 9.635211e+00, err= 2.022276e-08 xg[13]=0.81250, yg[11]=0.68750, u= 1.426362e+01, us= 1.426362e+01, err= 2.389466e-08 xg[13]=0.81250, yg[12]=0.75000, u= 2.111779e+01, us= 2.111779e+01, err= 2.755802e-08 xg[13]=0.81250, yg[13]=0.81250, u= 3.126726e+01, us= 3.126726e+01, err= 3.046125e-08 xg[13]=0.81250, yg[14]=0.87500, u= 4.629581e+01, us= 4.629581e+01, err= 3.179658e-08 xg[13]=0.81250, yg[15]=0.93750, u= 6.854855e+01, us= 6.854855e+01, err= 3.346487e-08 xg[13]=0.81250, yg[16]=1.00000, u= 1.014979e+02, us= 1.014979e+02, err= 0.000000e+00 xg[14]=0.87500, yg[ 0]=0.00000, u= 7.051332e-01, us= 7.051332e-01, err= 0.000000e+00 xg[14]=0.87500, yg[ 1]=0.06250, u= 7.601492e-01, us= 7.601492e-01, err= 3.165521e-08 xg[14]=0.87500, yg[ 2]=0.12500, u= 9.337821e-01, us= 9.337821e-01, err= 1.409993e-08 xg[14]=0.87500, yg[ 3]=0.18750, u= 1.253126e+00, us= 1.253126e+00, err= 3.770146e-09 xg[14]=0.87500, yg[ 4]=0.25000, u= 1.768013e+00, us= 1.768013e+00, err= 2.178441e-09 xg[14]=0.87500, yg[ 5]=0.31250, u= 2.558789e+00, us= 2.558789e+00, err= 5.840673e-09 xg[14]=0.87500, yg[ 6]=0.37500, u= 3.748849e+00, us= 3.748849e+00, err= 8.663670e-09 xg[14]=0.87500, yg[ 7]=0.43750, u= 5.523895e+00, us= 5.523895e+00, err= 1.147204e-08 xg[14]=0.87500, yg[ 8]=0.50000, u= 8.160912e+00, us= 8.160912e+00, err= 1.481495e-08 xg[14]=0.87500, yg[ 9]=0.56250, u= 1.207139e+01, us= 1.207139e+01, err= 1.910111e-08 xg[14]=0.87500, yg[10]=0.62500, u= 1.786554e+01, us= 1.786554e+01, err= 2.466025e-08 xg[14]=0.87500, yg[11]=0.68750, u= 2.644751e+01, us= 2.644751e+01, err= 3.168679e-08 xg[14]=0.87500, yg[12]=0.75000, u= 3.915646e+01, us= 3.915646e+01, err= 3.995790e-08 xg[14]=0.87500, yg[13]=0.81250, u= 5.797555e+01, us= 5.797555e+01, err= 4.831187e-08 xg[14]=0.87500, yg[14]=0.87500, u= 8.584138e+01, us= 8.584138e+01, err= 5.389387e-08 xg[14]=0.87500, yg[15]=0.93750, u= 1.271023e+02, us= 1.271023e+02, err= 5.731260e-08 xg[14]=0.87500, yg[16]=1.00000, u= 1.881967e+02, us= 1.881967e+02, err= 0.000000e+00 xg[15]=0.93750, yg[ 0]=0.00000, u= 9.227326e-01, us= 9.227326e-01, err= 0.000000e+00 xg[15]=0.93750, yg[ 1]=0.06250, u= 9.947262e-01, us= 9.947261e-01, err= 4.525388e-08 xg[15]=0.93750, yg[ 2]=0.12500, u= 1.221941e+00, us= 1.221941e+00, err= 1.516830e-08 xg[15]=0.93750, yg[ 3]=0.18750, u= 1.639833e+00, us= 1.639833e+00, err= 3.449039e-09 xg[15]=0.93750, yg[ 4]=0.25000, u= 2.313611e+00, us= 2.313611e+00, err= 1.815275e-09 xg[15]=0.93750, yg[ 5]=0.31250, u= 3.348414e+00, us= 3.348414e+00, err= 4.960513e-09 xg[15]=0.93750, yg[ 6]=0.37500, u= 4.905718e+00, us= 4.905718e+00, err= 7.651024e-09 xg[15]=0.93750, yg[ 7]=0.43750, u= 7.228532e+00, us= 7.228532e+00, err= 1.069288e-08 xg[15]=0.93750, yg[ 8]=0.50000, u= 1.067932e+01, us= 1.067932e+01, err= 1.474648e-08 xg[15]=0.93750, yg[ 9]=0.56250, u= 1.579654e+01, us= 1.579654e+01, err= 2.033811e-08 xg[15]=0.93750, yg[10]=0.62500, u= 2.337873e+01, us= 2.337873e+01, err= 2.814068e-08 xg[15]=0.93750, yg[11]=0.68750, u= 3.460904e+01, us= 3.460904e+01, err= 3.891317e-08 xg[15]=0.93750, yg[12]=0.75000, u= 5.123988e+01, us= 5.123988e+01, err= 5.323335e-08 xg[15]=0.93750, yg[13]=0.81250, u= 7.586641e+01, us= 7.586641e+01, err= 7.052015e-08 xg[15]=0.93750, yg[14]=0.87500, u= 1.123315e+02, us= 1.123315e+02, err= 8.470993e-08 xg[15]=0.93750, yg[15]=0.93750, u= 1.663252e+02, us= 1.663252e+02, err= 7.880010e-08 xg[15]=0.93750, yg[16]=1.00000, u= 2.462730e+02, us= 2.462730e+02, err= 0.000000e+00 xg[16]=1.00000, yg[ 0]=0.00000, u= 9.999949e-01, us= 9.999949e-01, err= 0.000000e+00 xg[16]=1.00000, yg[ 1]=0.06250, u= 1.078017e+00, us= 1.078017e+00, err= 0.000000e+00 xg[16]=1.00000, yg[ 2]=0.12500, u= 1.324257e+00, us= 1.324257e+00, err= 0.000000e+00 xg[16]=1.00000, yg[ 3]=0.18750, u= 1.777139e+00, us= 1.777139e+00, err= 0.000000e+00 xg[16]=1.00000, yg[ 4]=0.25000, u= 2.507334e+00, us= 2.507334e+00, err= 0.000000e+00 xg[16]=1.00000, yg[ 5]=0.31250, u= 3.628784e+00, us= 3.628784e+00, err= 0.000000e+00 xg[16]=1.00000, yg[ 6]=0.37500, u= 5.316484e+00, us= 5.316484e+00, err= 0.000000e+00 xg[16]=1.00000, yg[ 7]=0.43750, u= 7.833791e+00, us= 7.833791e+00, err= 0.000000e+00 xg[16]=1.00000, yg[ 8]=0.50000, u= 1.157352e+01, us= 1.157352e+01, err= 0.000000e+00 xg[16]=1.00000, yg[ 9]=0.56250, u= 1.711922e+01, us= 1.711922e+01, err= 0.000000e+00 xg[16]=1.00000, yg[10]=0.62500, u= 2.533628e+01, us= 2.533628e+01, err= 0.000000e+00 xg[16]=1.00000, yg[11]=0.68750, u= 3.750692e+01, us= 3.750692e+01, err= 0.000000e+00 xg[16]=1.00000, yg[12]=0.75000, u= 5.553030e+01, us= 5.553030e+01, err= 0.000000e+00 xg[16]=1.00000, yg[13]=0.81250, u= 8.221886e+01, us= 8.221886e+01, err= 0.000000e+00 xg[16]=1.00000, yg[14]=0.87500, u= 1.217372e+02, us= 1.217372e+02, err= 0.000000e+00 xg[16]=1.00000, yg[15]=0.93750, u= 1.802519e+02, us= 1.802519e+02, err= 0.000000e+00 xg[16]=1.00000, yg[16]=1.00000, u= 2.668939e+02, us= 2.668939e+02, err= 0.000000e+00 avg_error=4.3977e-06, max_error=9.93841e-08 writing pde_laplace_c.dat finished writing pde_laplace_c.dat finished pde_laplace.c