C 代码 应用有限差分法 （FDM） 到一个空间维度上的两点边界值问题 （BVP）.rar

26 February 2022 06:18:26 PM FD1D_BVP_TEST C version Test the FD1D_BVP library. FD1D_BVP_TEST01 A1(X) = 1.0 A1'(X) = 0.0 C1(X) = 0.0 F1(X) = X * ( X + 3 ) * exp ( X ) U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 21 X1 = 0.000000 X2 = 1.000000 I X U Uexact Error 0 0.000000 0.000000 0.000000 0.000000e+00 1 0.050000 0.049856 0.049935 7.983611e-05 2 0.100000 0.099310 0.099465 1.550978e-04 3 0.150000 0.147909 0.148134 2.253447e-04 4 0.200000 0.195134 0.195424 2.901004e-04 5 0.250000 0.240406 0.240755 3.488494e-04 6 0.300000 0.283069 0.283470 4.010347e-04 7 0.350000 0.322392 0.322838 4.460543e-04 8 0.400000 0.357555 0.358038 4.832581e-04 9 0.450000 0.387645 0.388157 5.119441e-04 10 0.500000 0.411649 0.412180 5.313552e-04 11 0.550000 0.428439 0.428980 5.406743e-04 12 0.600000 0.436769 0.437309 5.390206e-04 13 0.650000 0.435260 0.435786 5.254447e-04 14 0.700000 0.422389 0.422888 4.989239e-04 15 0.750000 0.396479 0.396938 4.583564e-04 16 0.800000 0.355684 0.356087 4.025562e-04 17 0.850000 0.297975 0.298305 3.302467e-04 18 0.900000 0.221124 0.221364 2.400542e-04 19 0.950000 0.122691 0.122821 1.305016e-04 20 1.000000 0.000000 0.000000 0.000000e+00 Repeat, using a nonuniform mesh. I X U Uexact Error 0 0.000000 0.000000 0.000000 0.000000e+00 1 0.223607 0.223398 0.217109 6.288990e-03 2 0.316228 0.302731 0.296652 6.079104e-03 3 0.387298 0.355237 0.349539 5.697365e-03 4 0.447214 0.391918 0.386629 5.288984e-03 5 0.500000 0.417063 0.412180 4.883151e-03 6 0.547723 0.432877 0.428389 4.487695e-03 7 0.591608 0.440664 0.436559 4.104582e-03 8 0.632456 0.441268 0.437534 3.733870e-03 9 0.670820 0.435265 0.431890 3.374959e-03 10 0.707107 0.423063 0.420036 3.027054e-03 11 0.741620 0.404963 0.402274 2.689328e-03 12 0.774597 0.381186 0.378825 2.361001e-03 13 0.806226 0.351900 0.349858 2.041354e-03 14 0.836660 0.317229 0.315499 1.729740e-03 15 0.866025 0.277269 0.275844 1.425575e-03 16 0.894427 0.232091 0.230963 1.128338e-03 17 0.921954 0.181745 0.180908 8.375612e-04 18 0.948683 0.126268 0.125715 5.528253e-04 19 0.974679 0.065682 0.065408 2.737520e-04 20 1.000000 0.000000 0.000000 0.000000e+00 FD1D_BVP_TEST02 A1(X) = 1.0 A1''(X) = 0.0 C2(X) = 2.0 F2(X) = X * ( 5 - X ) * exp ( X ) U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 X1 = 0.000000 X2 = 1.000000 I X U Uexact Error 0 0.000000 0.000000 0.000000 0.000000e+00 1 0.100000 0.098956 0.099465 5.090241e-04 2 0.200000 0.194477 0.195424 9.479345e-04 3 0.300000 0.282161 0.283470 1.309631e-03 4 0.400000 0.356455 0.358038 1.582792e-03 5 0.500000 0.410429 0.412180 1.751237e-03 6 0.600000 0.435515 0.437309 1.793133e-03 7 0.700000 0.421208 0.422888 1.680019e-03 8 0.800000 0.354711 0.356087 1.375625e-03 9 0.900000 0.220530 0.221364 8.344394e-04 10 1.000000 0.000000 0.000000 0.000000e+00 FD1D_BVP_TEST03 A1(X) = 1.0 A1''(X) = 0.0 C3(X) = 2.0 * X F3(X) = - X * ( 2 * X * X - 3 * X - 3 ) * exp ( X ) U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 X1 = 0.000000 X2 = 1.000000 I X U Uexact Error 0 0.000000 0.000000 0.000000 0.000000e+00 1 0.100000 0.098897 0.099465 5.682132e-04 2 0.200000 0.194367 0.195424 1.057269e-03 3 0.300000 0.282016 0.283470 1.454381e-03 4 0.400000 0.356292 0.358038 1.745490e-03 5 0.500000 0.410266 0.412180 1.914193e-03 6 0.600000 0.435368 0.437309 1.940463e-03 7 0.700000 0.421089 0.422888 1.799147e-03 8 0.800000 0.354628 0.356087 1.458138e-03 9 0.900000 0.220488 0.221364 8.761547e-04 10 1.000000 0.000000 0.000000 0.000000e+00 FD1D_BVP_TEST04 A2(X) = 1.0 + X * X A2''(X) = 2.0 * X C1(X) = 0.0 F4(X) = ( X + 3 X^2 + 5 X^3 + X^4 ) * exp ( X ) U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 X1 = 0.000000 X2 = 1.000000 I X U Uexact Error 0 0.000000 0.000000 0.000000 0.000000e+00 1 0.100000 0.098380 0.099465 1.085373e-03 2 0.200000 0.193367 0.195424 2.057252e-03 3 0.300000 0.280603 0.283470 2.866999e-03 4 0.400000 0.354572 0.358038 3.466284e-03 5 0.500000 0.408372 0.412180 3.808104e-03 6 0.600000 0.433462 0.437309 3.846521e-03 7 0.700000 0.419353 0.422888 3.535398e-03 8 0.800000 0.353260 0.356087 2.826537e-03 9 0.900000 0.219697 0.221364 1.667597e-03 10 1.000000 0.000000 0.000000 0.000000e+00 FD1D_BVP_TEST05 A3(X) = 1.0 + X * X for X <= 1/3 = 7/9 + X for 1/3 < X A3''(X) = 2.0 * X for X <= 1/3 1 for 1/3 < X C1(X) = 0.0 F5(X) = ( X + 3 X^2 + 5 X^3 + X^4 ) * exp ( X ) for X <= 1/3 = ( - 1 + 10/3 X + 43/9 X^2 + X^3 ) * exp ( X ) for 1/3 <= X U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 X1 = 0.000000 X2 = 1.000000 I X U Uexact Error 0 0.000000 0.000000 0.000000 0.000000e+00 1 0.100000 0.098419 0.099465 1.046676e-03 2 0.200000 0.193444 0.195424 1.980617e-03 3 0.300000 0.280716 0.283470 2.753858e-03 4 0.400000 0.354719 0.358038 3.318592e-03 5 0.500000 0.408578 0.412180 3.601826e-03 6 0.600000 0.433719 0.437309 3.589038e-03 7 0.700000 0.419631 0.422888 3.257460e-03 8 0.800000 0.353510 0.356087 2.576267e-03 9 0.900000 0.219858 0.221364 1.506382e-03 10 1.000000 0.000000 0.000000 0.000000e+00 FD1D_BVP_TEST Normal end of execution. 26 February 2022 06:18:26 PM