22 December 2011 11:21:19 AM FD1D_BVP_TEST C++ version 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 X2 = 1 I X U Uexact Error 0 0 0 0 0 1 0.05 0.0498555 0.0499354 7.98361e-05 2 0.1 0.0993103 0.0994654 0.000155098 3 0.15 0.147909 0.148134 0.000225345 4 0.2 0.195134 0.195424 0.0002901 5 0.25 0.240406 0.240755 0.000348849 6 0.3 0.283069 0.28347 0.000401035 7 0.35 0.322392 0.322838 0.000446054 8 0.4 0.357555 0.358038 0.000483258 9 0.45 0.387645 0.388157 0.000511944 10 0.5 0.411649 0.41218 0.000531355 11 0.55 0.428439 0.42898 0.000540674 12 0.6 0.436769 0.437309 0.000539021 13 0.65 0.43526 0.435786 0.000525445 14 0.7 0.422389 0.422888 0.000498924 15 0.75 0.396479 0.396938 0.000458356 16 0.8 0.355684 0.356087 0.000402556 17 0.85 0.297975 0.298305 0.000330247 18 0.9 0.221124 0.221364 0.000240054 19 0.95 0.122691 0.122821 0.000130502 20 1 0 0 0 Repeat, using a nonuniform mesh. I X U Uexact Error 0 0 0 0 0 1 0.223607 0.223398 0.217109 0.00628899 2 0.316228 0.302731 0.296652 0.0060791 3 0.387298 0.355237 0.349539 0.00569736 4 0.447214 0.391918 0.386629 0.00528898 5 0.5 0.417063 0.41218 0.00488315 6 0.547723 0.432877 0.428389 0.00448769 7 0.591608 0.440664 0.436559 0.00410458 8 0.632456 0.441268 0.437534 0.00373387 9 0.67082 0.435265 0.43189 0.00337496 10 0.707107 0.423063 0.420036 0.00302705 11 0.74162 0.404963 0.402274 0.00268933 12 0.774597 0.381186 0.378825 0.002361 13 0.806226 0.3519 0.349858 0.00204135 14 0.83666 0.317229 0.315499 0.00172974 15 0.866025 0.277269 0.275844 0.00142557 16 0.894427 0.232091 0.230963 0.00112834 17 0.921954 0.181745 0.180908 0.000837561 18 0.948683 0.126268 0.125715 0.000552825 19 0.974679 0.0656821 0.0654083 0.000273752 20 1 0 0 0 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 X2 = 1 I X U Uexact Error 0 0 0 0 0 1 0.1 0.0989564 0.0994654 0.000509024 2 0.2 0.194477 0.195424 0.000947935 3 0.3 0.282161 0.28347 0.00130963 4 0.4 0.356455 0.358038 0.00158279 5 0.5 0.410429 0.41218 0.00175124 6 0.6 0.435515 0.437309 0.00179313 7 0.7 0.421208 0.422888 0.00168002 8 0.8 0.354711 0.356087 0.00137563 9 0.9 0.22053 0.221364 0.000834439 10 1 0 0 0 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 X2 = 1 I X U Uexact Error 0 0 0 0 0 1 0.1 0.0988972 0.0994654 0.000568213 2 0.2 0.194367 0.195424 0.00105727 3 0.3 0.282016 0.28347 0.00145438 4 0.4 0.356292 0.358038 0.00174549 5 0.5 0.410266 0.41218 0.00191419 6 0.6 0.435368 0.437309 0.00194046 7 0.7 0.421089 0.422888 0.00179915 8 0.8 0.354628 0.356087 0.00145814 9 0.9 0.220488 0.221364 0.000876155 10 1 0 0 0 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 X2 = 1 I X U Uexact Error 0 0 0 0 0 1 0.1 0.09838 0.0994654 0.00108537 2 0.2 0.193367 0.195424 0.00205725 3 0.3 0.280603 0.28347 0.002867 4 0.4 0.354572 0.358038 0.00346628 5 0.5 0.408372 0.41218 0.0038081 6 0.6 0.433462 0.437309 0.00384652 7 0.7 0.419353 0.422888 0.0035354 8 0.8 0.35326 0.356087 0.00282654 9 0.9 0.219697 0.221364 0.0016676 10 1 0 0 0 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 X2 = 1 I X U Uexact Error 0 0 0 0 0 1 0.1 0.0984187 0.0994654 0.00104668 2 0.2 0.193444 0.195424 0.00198062 3 0.3 0.280716 0.28347 0.00275386 4 0.4 0.354719 0.358038 0.00331859 5 0.5 0.408578 0.41218 0.00360183 6 0.6 0.433719 0.437309 0.00358904 7 0.7 0.419631 0.422888 0.00325746 8 0.8 0.35351 0.356087 0.00257627 9 0.9 0.219858 0.221364 0.00150638 10 1 0 0 0 FD1D_BVP_TEST Normal end of execution. 22 December 2011 11:21:19 AM