corner0.c running differential equation to solve d^2u/dx^2 + d^2u/dy^2 = 0 uniform grid on rectangle -1,1 to -1,1 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)=-1.000000 xg( 1)=-0.800000 xg( 2)=-0.600000 xg( 3)=-0.400000 xg( 4)=-0.200000 xg( 5)=0.000000 xg( 6)=0.200000 xg( 7)=0.400000 xg( 8)=0.600000 xg( 9)=0.800000 xg(10)=1.000000 yg( 0)=-1.000000 yg( 1)=-0.800000 yg( 2)=-0.600000 yg( 3)=-0.400000 yg( 4)=-0.200000 yg( 5)=0.000000 yg( 6)=0.200000 yg( 7)=0.400000 yg( 8)=0.600000 yg( 9)=0.800000 yg(10)=1.000000 xmin=-1.000000, xmax=1.000000, hx=0.200000, nx=11 ymin=-1.000000, ymax=1.000000, hy=0.200000, 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=-0.0104871 row i= 1, j= 2, is bad err=-0.0416643 row i= 1, j= 3, is bad err=-0.365953 row i= 1, j= 4, is bad err=-4.07708 row i= 1, j= 5, is bad err=-93.9235 row i= 1, j= 6, is bad err=-4.07708 row i= 1, j= 7, is bad err=-0.365953 row i= 1, j= 8, is bad err=-0.0416643 row i= 1, j= 9, is bad err=-0.0104871 row i= 2, j= 1, is bad err=-0.0321511 row i= 2, j= 2, is bad err=0.0121105 row i= 2, j= 3, is bad err=0.0605265 row i= 2, j= 4, is bad err=0.692391 row i= 2, j= 5, is bad err=15.6442 row i= 2, j= 6, is bad err=0.692391 row i= 2, j= 7, is bad err=0.0605265 row i= 2, j= 8, is bad err=0.0121105 row i= 2, j= 9, is bad err=-0.0321511 row i= 3, j= 1, is bad err=-0.330396 row i= 3, j= 2, is bad err=0.0518334 row i= 3, j= 3, is bad err=-0.0312709 row i= 3, j= 4, is bad err=-0.153737 row i= 3, j= 5, is bad err=-2.55225 row i= 3, j= 6, is bad err=-0.153737 row i= 3, j= 7, is bad err=-0.0312709 row i= 3, j= 8, is bad err=0.0518334 row i= 3, j= 9, is bad err=-0.330396 row i= 4, j= 1, is bad err=-4.3195 row i= 4, j= 2, is bad err=0.721935 row i= 4, j= 3, is bad err=-0.187165 row i= 4, j= 4, is bad err=0.15692 row i= 4, j= 5, is bad err=-6.96686 row i= 4, j= 6, is bad err=0.15692 row i= 4, j= 7, is bad err=-0.187165 row i= 4, j= 8, is bad err=0.721935 row i= 4, j= 9, is bad err=-4.3195 row i= 5, j= 1, is bad err=-123.874 row i= 5, j= 2, is bad err=20.6033 row i= 5, j= 3, is bad err=-3.80208 row i= 5, j= 4, is bad err=-5.9958 row i= 5, j= 5, is bad err=37.5042 row i= 5, j= 6, is bad err=-5.9958 row i= 5, j= 7, is bad err=-3.80208 row i= 5, j= 8, is bad err=20.6033 row i= 5, j= 9, is bad err=-123.874 row i= 6, j= 1, is bad err=-63.5258 row i= 6, j= 2, is bad err=10.5866 row i= 6, j= 3, is bad err=-2.14981 row i= 6, j= 4, is bad err=-1.30296 row i= 6, j= 5, is bad err=12.0565 row i= 6, j= 6, is bad err=-1.30296 row i= 6, j= 7, is bad err=-2.14981 row i= 6, j= 8, is bad err=10.5866 row i= 6, j= 9, is bad err=-63.5258 row i= 7, j= 1, is bad err=-43.5684 row i= 7, j= 2, is bad err=7.25801 row i= 7, j= 3, is bad err=-1.4812 row i= 7, j= 4, is bad err=-1.13725 row i= 7, j= 5, is bad err=7.23351 row i= 7, j= 6, is bad err=-1.13725 row i= 7, j= 7, is bad err=-1.4812 row i= 7, j= 8, is bad err=7.25801 row i= 7, j= 9, is bad err=-43.5684 row i= 8, j= 1, is bad err=-35.0697 row i= 8, j= 2, is bad err=5.84192 row i= 8, j= 3, is bad err=-1.16976 row i= 8, j= 4, is bad err=-0.519137 row i= 8, j= 5, is bad err=21.7764 row i= 8, j= 6, is bad err=-0.519137 row i= 8, j= 7, is bad err=-1.16976 row i= 8, j= 8, is bad err=5.84192 row i= 8, j= 9, is bad err=-35.0697 row i= 9, j= 1, is bad err=-30.218 row i= 9, j= 2, is bad err=5.02902 row i= 9, j= 3, is bad err=-1.11974 row i= 9, j= 4, is bad err=-2.76844 row i= 9, j= 5, is bad err=-74.0668 row i= 9, j= 6, is bad err=-2.76844 row i= 9, j= 7, is bad err=-1.11974 row i= 9, j= 8, is bad err=5.02902 row i= 9, j= 9, is bad err=-30.218 check_soln against PDE check soln against PDE max error=2.34035e-11 exact solution u, computed us, error xg[ 0]=-1.00000, yg[ 0]=-1.00000, u= 1.098684e+00, us= 1.098684e+00, err= 0.000000e+00 xg[ 0]=-1.00000, yg[ 1]=-0.80000, u= 1.067854e+00, us= 1.067854e+00, err= 0.000000e+00 xg[ 0]=-1.00000, yg[ 2]=-0.60000, u= 1.040719e+00, us= 1.040719e+00, err= 0.000000e+00 xg[ 0]=-1.00000, yg[ 3]=-0.40000, u= 1.019076e+00, us= 1.019076e+00, err= 0.000000e+00 xg[ 0]=-1.00000, yg[ 4]=-0.20000, u= 1.004939e+00, us= 1.004939e+00, err= 0.000000e+00 xg[ 0]=-1.00000, yg[ 5]=0.00000, u= 1.000000e+00, us= 1.000000e+00, err= 0.000000e+00 xg[ 0]=-1.00000, yg[ 6]=0.20000, u= 1.004939e+00, us= 1.004939e+00, err= 0.000000e+00 xg[ 0]=-1.00000, yg[ 7]=0.40000, u= 1.019076e+00, us= 1.019076e+00, err= 0.000000e+00 xg[ 0]=-1.00000, yg[ 8]=0.60000, u= 1.040719e+00, us= 1.040719e+00, err= 0.000000e+00 xg[ 0]=-1.00000, yg[ 9]=0.80000, u= 1.067854e+00, us= 1.067854e+00, err= 0.000000e+00 xg[ 0]=-1.00000, yg[10]=1.00000, u= 1.098684e+00, us= 1.098684e+00, err= 0.000000e+00 xg[ 1]=-0.80000, yg[ 0]=-1.00000, u= 1.019957e+00, us= 1.019957e+00, err= 0.000000e+00 xg[ 1]=-0.80000, yg[ 1]=-0.80000, u= 9.826929e-01, us= 9.949683e-01, err= 1.227534e-02 xg[ 1]=-0.80000, yg[ 2]=-0.60000, u= 9.486833e-01, us= 9.745535e-01, err= 2.587019e-02 xg[ 1]=-0.80000, yg[ 3]=-0.40000, u= 9.204421e-01, us= 9.576906e-01, err= 3.724855e-02 xg[ 1]=-0.80000, yg[ 4]=-0.20000, u= 9.012827e-01, us= 9.466889e-01, err= 4.540614e-02 xg[ 1]=-0.80000, yg[ 5]=0.00000, u= 8.944272e-01, us= 9.429781e-01, err= 4.855090e-02 xg[ 1]=-0.80000, yg[ 6]=0.20000, u= 9.012827e-01, us= 9.466889e-01, err= 4.540614e-02 xg[ 1]=-0.80000, yg[ 7]=0.40000, u= 9.204421e-01, us= 9.576906e-01, err= 3.724855e-02 xg[ 1]=-0.80000, yg[ 8]=0.60000, u= 9.486833e-01, us= 9.745535e-01, err= 2.587019e-02 xg[ 1]=-0.80000, yg[ 9]=0.80000, u= 9.826929e-01, us= 9.949683e-01, err= 1.227534e-02 xg[ 1]=-0.80000, yg[10]=1.00000, u= 1.019957e+00, us= 1.019957e+00, err= 0.000000e+00 xg[ 2]=-0.60000, yg[ 0]=-1.00000, u= 9.397314e-01, us= 9.397314e-01, err= 0.000000e+00 xg[ 2]=-0.60000, yg[ 1]=-0.80000, u= 8.944272e-01, us= 9.208688e-01, err= 2.644158e-02 xg[ 2]=-0.60000, yg[ 2]=-0.60000, u= 8.510371e-01, us= 9.037956e-01, err= 5.275859e-02 xg[ 2]=-0.60000, yg[ 3]=-0.40000, u= 8.127454e-01, us= 8.901345e-01, err= 7.738907e-02 xg[ 2]=-0.60000, yg[ 4]=-0.20000, u= 7.850018e-01, us= 8.812313e-01, err= 9.622950e-02 xg[ 2]=-0.60000, yg[ 5]=0.00000, u= 7.745967e-01, us= 8.781436e-01, err= 1.035469e-01 xg[ 2]=-0.60000, yg[ 6]=0.20000, u= 7.850018e-01, us= 8.812313e-01, err= 9.622950e-02 xg[ 2]=-0.60000, yg[ 7]=0.40000, u= 8.127454e-01, us= 8.901345e-01, err= 7.738907e-02 xg[ 2]=-0.60000, yg[ 8]=0.60000, u= 8.510371e-01, us= 9.037956e-01, err= 5.275859e-02 xg[ 2]=-0.60000, yg[ 9]=0.80000, u= 8.944272e-01, us= 9.208688e-01, err= 2.644158e-02 xg[ 2]=-0.60000, yg[10]=1.00000, u= 9.397314e-01, us= 9.397314e-01, err= 0.000000e+00 xg[ 3]=-0.40000, yg[ 0]=-1.00000, u= 8.593698e-01, us= 8.593698e-01, err= 0.000000e+00 xg[ 3]=-0.40000, yg[ 1]=-0.80000, u= 8.044959e-01, us= 8.444053e-01, err= 3.990948e-02 xg[ 3]=-0.40000, yg[ 2]=-0.60000, u= 7.487023e-01, us= 8.298116e-01, err= 8.110929e-02 xg[ 3]=-0.40000, yg[ 3]=-0.40000, u= 6.948688e-01, us= 8.177424e-01, err= 1.228736e-01 xg[ 3]=-0.40000, yg[ 4]=-0.20000, u= 6.508508e-01, us= 8.098098e-01, err= 1.589589e-01 xg[ 3]=-0.40000, yg[ 5]=0.00000, u= 6.324555e-01, us= 8.070476e-01, err= 1.745920e-01 xg[ 3]=-0.40000, yg[ 6]=0.20000, u= 6.508508e-01, us= 8.098098e-01, err= 1.589589e-01 xg[ 3]=-0.40000, yg[ 7]=0.40000, u= 6.948688e-01, us= 8.177424e-01, err= 1.228736e-01 xg[ 3]=-0.40000, yg[ 8]=0.60000, u= 7.487023e-01, us= 8.298116e-01, err= 8.110929e-02 xg[ 3]=-0.40000, yg[ 9]=0.80000, u= 8.044959e-01, us= 8.444053e-01, err= 3.990948e-02 xg[ 3]=-0.40000, yg[10]=1.00000, u= 8.593698e-01, us= 8.593698e-01, err= 0.000000e+00 xg[ 4]=-0.20000, yg[ 0]=-1.00000, u= 7.809622e-01, us= 7.809622e-01, err= 0.000000e+00 xg[ 4]=-0.20000, yg[ 1]=-0.80000, u= 7.157587e-01, us= 7.674591e-01, err= 5.170036e-02 xg[ 4]=-0.20000, yg[ 2]=-0.60000, u= 6.451572e-01, us= 7.532078e-01, err= 1.080507e-01 xg[ 4]=-0.20000, yg[ 3]=-0.40000, u= 5.688645e-01, us= 7.411201e-01, err= 1.722556e-01 xg[ 4]=-0.20000, yg[ 4]=-0.20000, u= 4.913465e-01, us= 7.331052e-01, err= 2.417587e-01 xg[ 4]=-0.20000, yg[ 5]=0.00000, u= 4.472136e-01, us= 7.303029e-01, err= 2.830894e-01 xg[ 4]=-0.20000, yg[ 6]=0.20000, u= 4.913465e-01, us= 7.331052e-01, err= 2.417587e-01 xg[ 4]=-0.20000, yg[ 7]=0.40000, u= 5.688645e-01, us= 7.411201e-01, err= 1.722556e-01 xg[ 4]=-0.20000, yg[ 8]=0.60000, u= 6.451572e-01, us= 7.532078e-01, err= 1.080507e-01 xg[ 4]=-0.20000, yg[ 9]=0.80000, u= 7.157587e-01, us= 7.674591e-01, err= 5.170036e-02 xg[ 4]=-0.20000, yg[10]=1.00000, u= 7.809622e-01, us= 7.809622e-01, err= 0.000000e+00 xg[ 5]=0.00000, yg[ 0]=-1.00000, u= 7.071068e-01, us= 7.071068e-01, err= 0.000000e+00 xg[ 5]=0.00000, yg[ 1]=-0.80000, u= 6.324555e-01, us= 6.910497e-01, err= 5.859416e-02 xg[ 5]=0.00000, yg[ 2]=-0.60000, u= 5.477226e-01, us= 6.742775e-01, err= 1.265549e-01 xg[ 5]=0.00000, yg[ 3]=-0.40000, u= 4.472136e-01, us= 6.603048e-01, err= 2.130913e-01 xg[ 5]=0.00000, yg[ 4]=-0.20000, u= 3.162278e-01, us= 6.510636e-01, err= 3.348358e-01 xg[ 5]=0.00000, yg[ 5]=0.00000, u= 0.000000e+00, us= 6.478207e-01, err= 6.478207e-01 xg[ 5]=0.00000, yg[ 6]=0.20000, u= 3.162278e-01, us= 6.510636e-01, err= 3.348358e-01 xg[ 5]=0.00000, yg[ 7]=0.40000, u= 4.472136e-01, us= 6.603048e-01, err= 2.130913e-01 xg[ 5]=0.00000, yg[ 8]=0.60000, u= 5.477226e-01, us= 6.742775e-01, err= 1.265549e-01 xg[ 5]=0.00000, yg[ 9]=0.80000, u= 6.324555e-01, us= 6.910497e-01, err= 5.859416e-02 xg[ 5]=0.00000, yg[10]=1.00000, u= 7.071068e-01, us= 7.071068e-01, err= 0.000000e+00 xg[ 6]=0.20000, yg[ 0]=-1.00000, u= 6.402359e-01, us= 6.402359e-01, err= 0.000000e+00 xg[ 6]=0.20000, yg[ 1]=-0.80000, u= 5.588475e-01, us= 6.147414e-01, err= 5.589385e-02 xg[ 6]=0.20000, yg[ 2]=-0.60000, u= 4.650030e-01, us= 5.923298e-01, err= 1.273269e-01 xg[ 6]=0.20000, yg[ 3]=-0.40000, u= 3.515776e-01, us= 5.746792e-01, err= 2.231016e-01 xg[ 6]=0.20000, yg[ 4]=-0.20000, u= 2.035224e-01, us= 5.628925e-01, err= 3.593701e-01 xg[ 6]=0.20000, yg[ 5]=0.00000, u= 6.206335e-17, us= 5.586741e-01, err= 5.586741e-01 xg[ 6]=0.20000, yg[ 6]=0.20000, u= 2.035224e-01, us= 5.628925e-01, err= 3.593701e-01 xg[ 6]=0.20000, yg[ 7]=0.40000, u= 3.515776e-01, us= 5.746792e-01, err= 2.231016e-01 xg[ 6]=0.20000, yg[ 8]=0.60000, u= 4.650030e-01, us= 5.923298e-01, err= 1.273269e-01 xg[ 6]=0.20000, yg[ 9]=0.80000, u= 5.588475e-01, us= 6.147414e-01, err= 5.589385e-02 xg[ 6]=0.20000, yg[10]=1.00000, u= 6.402359e-01, us= 6.402359e-01, err= 0.000000e+00 xg[ 7]=0.40000, yg[ 0]=-1.00000, u= 5.818217e-01, us= 5.818217e-01, err= 0.000000e+00 xg[ 7]=0.40000, yg[ 1]=-0.80000, u= 4.972058e-01, us= 5.341047e-01, err= 3.689889e-02 xg[ 7]=0.40000, yg[ 2]=-0.60000, u= 4.006933e-01, us= 5.057051e-01, err= 1.050118e-01 xg[ 7]=0.40000, yg[ 3]=-0.40000, u= 2.878241e-01, us= 4.833617e-01, err= 1.955376e-01 xg[ 7]=0.40000, yg[ 4]=-0.20000, u= 1.536450e-01, us= 4.669911e-01, err= 3.133461e-01 xg[ 7]=0.40000, yg[ 5]=0.00000, u= 4.388542e-17, us= 4.607336e-01, err= 4.607336e-01 xg[ 7]=0.40000, yg[ 6]=0.20000, u= 1.536450e-01, us= 4.669911e-01, err= 3.133461e-01 xg[ 7]=0.40000, yg[ 7]=0.40000, u= 2.878241e-01, us= 4.833617e-01, err= 1.955376e-01 xg[ 7]=0.40000, yg[ 8]=0.60000, u= 4.006933e-01, us= 5.057051e-01, err= 1.050118e-01 xg[ 7]=0.40000, yg[ 9]=0.80000, u= 4.972058e-01, us= 5.341047e-01, err= 3.689889e-02 xg[ 7]=0.40000, yg[10]=1.00000, u= 5.818217e-01, us= 5.818217e-01, err= 0.000000e+00 xg[ 8]=0.60000, yg[ 0]=-1.00000, u= 5.320669e-01, us= 5.320669e-01, err= 0.000000e+00 xg[ 8]=0.60000, yg[ 1]=-0.80000, u= 4.472136e-01, us= 4.372718e-01, err= 9.941831e-03 xg[ 8]=0.60000, yg[ 2]=-0.60000, u= 3.525111e-01, us= 4.149767e-01, err= 6.246559e-02 xg[ 8]=0.60000, yg[ 3]=-0.40000, u= 2.460795e-01, us= 3.867678e-01, err= 1.406883e-01 xg[ 8]=0.60000, yg[ 4]=-0.20000, u= 1.273882e-01, us= 3.606104e-01, err= 2.332222e-01 xg[ 8]=0.60000, yg[ 5]=0.00000, u= 3.583229e-17, us= 3.492635e-01, err= 3.492635e-01 xg[ 8]=0.60000, yg[ 6]=0.20000, u= 1.273882e-01, us= 3.606104e-01, err= 2.332222e-01 xg[ 8]=0.60000, yg[ 7]=0.40000, u= 2.460795e-01, us= 3.867678e-01, err= 1.406883e-01 xg[ 8]=0.60000, yg[ 8]=0.60000, u= 3.525111e-01, us= 4.149767e-01, err= 6.246559e-02 xg[ 8]=0.60000, yg[ 9]=0.80000, u= 4.472136e-01, us= 4.372718e-01, err= 9.941831e-03 xg[ 8]=0.60000, yg[10]=1.00000, u= 5.320669e-01, us= 5.320669e-01, err= 0.000000e+00 xg[ 9]=0.80000, yg[ 0]=-1.00000, u= 4.902167e-01, us= 4.902167e-01, err= 0.000000e+00 xg[ 9]=0.80000, yg[ 1]=-0.80000, u= 4.070447e-01, us= 3.237004e-01, err= 8.334436e-02 xg[ 9]=0.80000, yg[ 2]=-0.60000, u= 3.162278e-01, us= 3.340093e-01, err= 1.778155e-02 xg[ 9]=0.80000, yg[ 3]=-0.40000, u= 2.172869e-01, us= 2.889195e-01, err= 7.163264e-02 xg[ 9]=0.80000, yg[ 4]=-0.20000, u= 1.109530e-01, us= 2.390359e-01, err= 1.280829e-01 xg[ 9]=0.80000, yg[ 5]=0.00000, u= 3.103168e-17, us= 2.111930e-01, err= 2.111930e-01 xg[ 9]=0.80000, yg[ 6]=0.20000, u= 1.109530e-01, us= 2.390359e-01, err= 1.280829e-01 xg[ 9]=0.80000, yg[ 7]=0.40000, u= 2.172869e-01, us= 2.889195e-01, err= 7.163264e-02 xg[ 9]=0.80000, yg[ 8]=0.60000, u= 3.162278e-01, us= 3.340093e-01, err= 1.778155e-02 xg[ 9]=0.80000, yg[ 9]=0.80000, u= 4.070447e-01, us= 3.237004e-01, err= 8.334436e-02 xg[ 9]=0.80000, yg[10]=1.00000, u= 4.902167e-01, us= 4.902167e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 0]=-1.00000, u= 4.550899e-01, us= 4.550899e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 1]=-0.80000, u= 3.745830e-01, us= 3.745830e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 2]=-0.60000, u= 2.882624e-01, us= 2.882624e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 3]=-0.40000, u= 1.962562e-01, us= 1.962562e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 4]=-0.20000, u= 9.950855e-02, us= 9.950855e-02, err= 0.000000e+00 xg[10]=1.00000, yg[ 5]=0.00000, u= 2.775558e-17, us= 2.775558e-17, err= 0.000000e+00 xg[10]=1.00000, yg[ 6]=0.20000, u= 9.950855e-02, us= 9.950855e-02, err= 0.000000e+00 xg[10]=1.00000, yg[ 7]=0.40000, u= 1.962562e-01, us= 1.962562e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 8]=0.60000, u= 2.882624e-01, us= 2.882624e-01, err= 0.000000e+00 xg[10]=1.00000, yg[ 9]=0.80000, u= 3.745830e-01, us= 3.745830e-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=11.3314, max_error=0.647821 writing corner0_c.dat finished writing corner0_c.dat finished corner0.c in 0.040000 seconds