pde22_eq.c running differential equation to solve d^2u/dx^2 + d^2u/dy^2 = c(x,y) Uxx(x,y) = 2^16 * 12*x^2 * (1-x)^4 * y^4 * (1-y)^4 - 32*x^3 * (1-x)^3 * y^4 * (1-y)^4 + 12*x^4 * (1-x)^2 * y^4 * (1-y)^4; Uyy(x,y) = 2^16 * 12*x^4 * (1-x)^4 * y^2 * (1-y)^4 - 32*x^4 * (1-x)^4 * y^3 * (1-y)^3 + 12*x^4 * (1-x)^4 * y^4 * (1-y)^2; c(x,y) = Uxx(x,y) + Uyy(x,y); uniform grid on rectangle 0,1 to 0,1 known Solution, for testing method u(x,y) = 2^16*x^4*(1-x)^4*y^4*(1-y)4 xg( 0)=0.000000 xg( 1)=0.111111 xg( 2)=0.222222 xg( 3)=0.333333 xg( 4)=0.444444 xg( 5)=0.555556 xg( 6)=0.666667 xg( 7)=0.777778 xg( 8)=0.888889 xg( 9)=1.000000 yg( 0)=0.000000 yg( 1)=0.111111 yg( 2)=0.222222 yg( 3)=0.333333 yg( 4)=0.444444 yg( 5)=0.555556 yg( 6)=0.666667 yg( 7)=0.777778 yg( 8)=0.888889 yg( 9)=1.000000 xmin=0.000000, xmax=1.000000, hx=0.111111, nx=10 ymin=0.000000, ymax=1.000000, hy=0.111111, ny=10 u(0.5,0.5)=1.000000 c(0.5,0.5)=-64.000000 internal cells zeroed matrix initialized check_soln against PDE check soln against PDE max error=7.13646e-12 exact solution u, computed us, error xg[ 0]=0.00000, yg[ 0]=0.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 1]=0.11111, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 2]=0.22222, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 3]=0.33333, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 4]=0.44444, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 5]=0.55556, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 6]=0.66667, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 7]=0.77778, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 8]=0.88889, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 0]=0.00000, yg[ 9]=1.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 1]=0.11111, yg[ 0]=0.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 1]=0.11111, yg[ 1]=0.11111, u= 5.933619e-04, us= 5.933619e-04, err= 1.648907e-12 xg[ 1]=0.11111, yg[ 2]=0.22222, u= 5.565086e-03, us= 5.565086e-03, err= 3.705919e-12 xg[ 1]=0.11111, yg[ 3]=0.33333, u= 1.520722e-02, us= 1.520722e-02, err= 5.597480e-12 xg[ 1]=0.11111, yg[ 4]=0.44444, u= 2.317820e-02, us= 2.317820e-02, err= 7.532076e-12 xg[ 1]=0.11111, yg[ 5]=0.55556, u= 2.317820e-02, us= 2.317820e-02, err= 9.585176e-12 xg[ 1]=0.11111, yg[ 6]=0.66667, u= 1.520722e-02, us= 1.520722e-02, err= 1.102610e-11 xg[ 1]=0.11111, yg[ 7]=0.77778, u= 5.565086e-03, us= 5.565086e-03, err= 1.013168e-11 xg[ 1]=0.11111, yg[ 8]=0.88889, u= 5.933619e-04, us= 5.933619e-04, err= 5.821826e-12 xg[ 1]=0.11111, yg[ 9]=1.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 2]=0.22222, yg[ 0]=0.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 2]=0.22222, yg[ 1]=0.11111, u= 5.565086e-03, us= 5.565086e-03, err= 3.705097e-12 xg[ 2]=0.22222, yg[ 2]=0.22222, u= 5.219442e-02, us= 5.219442e-02, err= 9.205142e-12 xg[ 2]=0.22222, yg[ 3]=0.33333, u= 1.426271e-01, us= 1.426271e-01, err= 1.462579e-11 xg[ 2]=0.22222, yg[ 4]=0.44444, u= 2.173862e-01, us= 2.173862e-01, err= 1.983358e-11 xg[ 2]=0.22222, yg[ 5]=0.55556, u= 2.173862e-01, us= 2.173862e-01, err= 2.452871e-11 xg[ 2]=0.22222, yg[ 6]=0.66667, u= 1.426271e-01, us= 1.426271e-01, err= 2.744566e-11 xg[ 2]=0.22222, yg[ 7]=0.77778, u= 5.219442e-02, us= 5.219442e-02, err= 2.473893e-11 xg[ 2]=0.22222, yg[ 8]=0.88889, u= 5.565086e-03, us= 5.565086e-03, err= 1.338609e-11 xg[ 2]=0.22222, yg[ 9]=1.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 3]=0.33333, yg[ 0]=0.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 3]=0.33333, yg[ 1]=0.11111, u= 1.520722e-02, us= 1.520722e-02, err= 5.597752e-12 xg[ 3]=0.33333, yg[ 2]=0.22222, u= 1.426271e-01, us= 1.426271e-01, err= 1.462446e-11 xg[ 3]=0.33333, yg[ 3]=0.33333, u= 3.897443e-01, us= 3.897443e-01, err= 2.347734e-11 xg[ 3]=0.33333, yg[ 4]=0.44444, u= 5.940319e-01, us= 5.940319e-01, err= 3.186763e-11 xg[ 3]=0.33333, yg[ 5]=0.55556, u= 5.940319e-01, us= 5.940319e-01, err= 3.946666e-11 xg[ 3]=0.33333, yg[ 6]=0.66667, u= 3.897443e-01, us= 3.897443e-01, err= 4.475063e-11 xg[ 3]=0.33333, yg[ 7]=0.77778, u= 1.426271e-01, us= 1.426271e-01, err= 4.088145e-11 xg[ 3]=0.33333, yg[ 8]=0.88889, u= 1.520722e-02, us= 1.520722e-02, err= 2.142131e-11 xg[ 3]=0.33333, yg[ 9]=1.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 4]=0.44444, yg[ 0]=0.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 4]=0.44444, yg[ 1]=0.11111, u= 2.317820e-02, us= 2.317820e-02, err= 7.528807e-12 xg[ 4]=0.44444, yg[ 2]=0.22222, u= 2.173862e-01, us= 2.173862e-01, err= 1.983088e-11 xg[ 4]=0.44444, yg[ 3]=0.33333, u= 5.940319e-01, us= 5.940319e-01, err= 3.186696e-11 xg[ 4]=0.44444, yg[ 4]=0.44444, u= 9.053984e-01, us= 9.053984e-01, err= 4.296567e-11 xg[ 4]=0.44444, yg[ 5]=0.55556, u= 9.053984e-01, us= 9.053984e-01, err= 5.256311e-11 xg[ 4]=0.44444, yg[ 6]=0.66667, u= 5.940319e-01, us= 5.940319e-01, err= 5.906367e-11 xg[ 4]=0.44444, yg[ 7]=0.77778, u= 2.173862e-01, us= 2.173862e-01, err= 5.370248e-11 xg[ 4]=0.44444, yg[ 8]=0.88889, u= 2.317820e-02, us= 2.317820e-02, err= 2.760263e-11 xg[ 4]=0.44444, yg[ 9]=1.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 5]=0.55556, yg[ 0]=0.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 5]=0.55556, yg[ 1]=0.11111, u= 2.317820e-02, us= 2.317820e-02, err= 9.581523e-12 xg[ 5]=0.55556, yg[ 2]=0.22222, u= 2.173862e-01, us= 2.173862e-01, err= 2.452865e-11 xg[ 5]=0.55556, yg[ 3]=0.33333, u= 5.940319e-01, us= 5.940319e-01, err= 3.946688e-11 xg[ 5]=0.55556, yg[ 4]=0.44444, u= 9.053984e-01, us= 9.053984e-01, err= 5.256233e-11 xg[ 5]=0.55556, yg[ 5]=0.55556, u= 9.053984e-01, us= 9.053984e-01, err= 6.215910e-11 xg[ 5]=0.55556, yg[ 6]=0.66667, u= 5.940319e-01, us= 5.940319e-01, err= 6.666504e-11 xg[ 5]=0.55556, yg[ 7]=0.77778, u= 2.173862e-01, us= 2.173862e-01, err= 5.840019e-11 xg[ 5]=0.55556, yg[ 8]=0.88889, u= 2.317820e-02, us= 2.317820e-02, err= 2.965140e-11 xg[ 5]=0.55556, yg[ 9]=1.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 6]=0.66667, yg[ 0]=0.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 6]=0.66667, yg[ 1]=0.11111, u= 1.520722e-02, us= 1.520722e-02, err= 1.102591e-11 xg[ 6]=0.66667, yg[ 2]=0.22222, u= 1.426271e-01, us= 1.426271e-01, err= 2.744721e-11 xg[ 6]=0.66667, yg[ 3]=0.33333, u= 3.897443e-01, us= 3.897443e-01, err= 4.474825e-11 xg[ 6]=0.66667, yg[ 4]=0.44444, u= 5.940319e-01, us= 5.940319e-01, err= 5.906323e-11 xg[ 6]=0.66667, yg[ 5]=0.55556, u= 5.940319e-01, us= 5.940319e-01, err= 6.666537e-11 xg[ 6]=0.66667, yg[ 6]=0.66667, u= 3.897443e-01, us= 3.897443e-01, err= 6.602510e-11 xg[ 6]=0.66667, yg[ 7]=0.77778, u= 1.426271e-01, us= 1.426271e-01, err= 5.370889e-11 xg[ 6]=0.66667, yg[ 8]=0.88889, u= 1.520722e-02, us= 1.520722e-02, err= 2.685418e-11 xg[ 6]=0.66667, yg[ 9]=1.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 7]=0.77778, yg[ 0]=0.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 7]=0.77778, yg[ 1]=0.11111, u= 5.565086e-03, us= 5.565086e-03, err= 1.013124e-11 xg[ 7]=0.77778, yg[ 2]=0.22222, u= 5.219442e-02, us= 5.219442e-02, err= 2.473650e-11 xg[ 7]=0.77778, yg[ 3]=0.33333, u= 1.426271e-01, us= 1.426271e-01, err= 4.087912e-11 xg[ 7]=0.77778, yg[ 4]=0.44444, u= 2.173862e-01, us= 2.173862e-01, err= 5.370098e-11 xg[ 7]=0.77778, yg[ 5]=0.55556, u= 2.173862e-01, us= 2.173862e-01, err= 5.840083e-11 xg[ 7]=0.77778, yg[ 6]=0.66667, u= 1.426271e-01, us= 1.426271e-01, err= 5.370992e-11 xg[ 7]=0.77778, yg[ 7]=0.77778, u= 5.219442e-02, us= 5.219442e-02, err= 4.028391e-11 xg[ 7]=0.77778, yg[ 8]=0.88889, u= 5.565086e-03, us= 5.565086e-03, err= 1.983302e-11 xg[ 7]=0.77778, yg[ 9]=1.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 8]=0.88889, yg[ 0]=0.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 8]=0.88889, yg[ 1]=0.11111, u= 5.933619e-04, us= 5.933619e-04, err= 5.817390e-12 xg[ 8]=0.88889, yg[ 2]=0.22222, u= 5.565086e-03, us= 5.565086e-03, err= 1.339023e-11 xg[ 8]=0.88889, yg[ 3]=0.33333, u= 1.520722e-02, us= 1.520722e-02, err= 2.141839e-11 xg[ 8]=0.88889, yg[ 4]=0.44444, u= 2.317820e-02, us= 2.317820e-02, err= 2.760122e-11 xg[ 8]=0.88889, yg[ 5]=0.55556, u= 2.317820e-02, us= 2.317820e-02, err= 2.965386e-11 xg[ 8]=0.88889, yg[ 6]=0.66667, u= 1.520722e-02, us= 1.520722e-02, err= 2.685801e-11 xg[ 8]=0.88889, yg[ 7]=0.77778, u= 5.565086e-03, us= 5.565086e-03, err= 1.983815e-11 xg[ 8]=0.88889, yg[ 8]=0.88889, u= 5.933619e-04, us= 5.933619e-04, err= 1.002696e-11 xg[ 8]=0.88889, yg[ 9]=1.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 9]=1.00000, yg[ 0]=0.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 9]=1.00000, yg[ 1]=0.11111, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 9]=1.00000, yg[ 2]=0.22222, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 9]=1.00000, yg[ 3]=0.33333, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 9]=1.00000, yg[ 4]=0.44444, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 9]=1.00000, yg[ 5]=0.55556, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 9]=1.00000, yg[ 6]=0.66667, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 9]=1.00000, yg[ 7]=0.77778, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 9]=1.00000, yg[ 8]=0.88889, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 xg[ 9]=1.00000, yg[ 9]=1.00000, u= 0.000000e+00, us= 0.000000e+00, err= 0.000000e+00 avg_error=1.86456e-09, max_error=6.66654e-11 writing pde22_eq_c.dat finished writing pde22_eq_c.dat finished pde22_eq.c in 0.020000 seconds