19 February 2012 3:12:10.849 PM FEM1D_BVP_LINEAR_PRB FORTRAN77 version Test the FEM1D_BVP_LINEAR library. FEM1D_BVP_LINEAR_TEST01 A1(X) = 1.0 C1(X) = 0.0 F1(X) = X * ( X + 3 ) * exp ( X ) U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 I X U Uexact Error 1 0.00 0.499600E-15 0.00000 0.499600E-15 2 0.10 0.994655E-01 0.994654E-01 0.133423E-06 3 0.20 0.195425 0.195424 0.247563E-06 4 0.30 0.283471 0.283470 0.339433E-06 5 0.40 0.358038 0.358038 0.405613E-06 6 0.50 0.412181 0.412180 0.442187E-06 7 0.60 0.437309 0.437309 0.444681E-06 8 0.70 0.422888 0.422888 0.407976E-06 9 0.80 0.356087 0.356087 0.326231E-06 10 0.90 0.221364 0.221364 0.192775E-06 11 1.00 0.00000 0.00000 0.00000 L2 norm of error = 0.400665E-02 Seminorm of error = 0.138667 FEM1D_BVP_LINEAR_TEST02 A1(X) = 1.0 C2(X) = 2.0 F2(X) = X * ( 5 - X ) * exp ( X ) U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 I X U Uexact Error 1 0.00 0.555112E-16 0.00000 0.555112E-16 2 0.10 0.995976E-01 0.994654E-01 0.132179E-03 3 0.20 0.195686 0.195424 0.261061E-03 4 0.30 0.283852 0.283470 0.381845E-03 5 0.40 0.358526 0.358038 0.487632E-03 6 0.50 0.412749 0.412180 0.568904E-03 7 0.60 0.437921 0.437309 0.612904E-03 8 0.70 0.423491 0.422888 0.602870E-03 9 0.80 0.356604 0.356087 0.517106E-03 10 0.90 0.221692 0.221364 0.327866E-03 11 1.00 0.00000 0.00000 0.00000 L2 norm of error = 0.369835E-02 Seminorm of error = 0.138675 FEM1D_BVP_LINEAR_TEST03 A1(X) = 1.0 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 I X U Uexact Error 1 0.00 0.166533E-15 0.00000 0.166533E-15 2 0.10 0.995489E-01 0.994654E-01 0.835035E-04 3 0.20 0.195591 0.195424 0.166483E-03 4 0.30 0.283718 0.283470 0.247341E-03 5 0.40 0.358361 0.358038 0.322738E-03 6 0.50 0.412567 0.412180 0.386818E-03 7 0.60 0.437739 0.437309 0.430206E-03 8 0.70 0.423327 0.422888 0.438689E-03 9 0.80 0.356478 0.356087 0.391498E-03 10 0.90 0.221623 0.221364 0.259052E-03 11 1.00 0.00000 0.00000 0.00000 L2 norm of error = 0.377892E-02 Seminorm of error = 0.138671 FEM1D_BVP_LINEAR_TEST04 A2(X) = 1.0 + X * 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 I X U Uexact Error 1 0.00 -0.138778E-14 0.00000 0.138778E-14 2 0.10 0.998202E-01 0.994654E-01 0.354837E-03 3 0.20 0.196115 0.195424 0.690400E-03 4 0.30 0.284455 0.283470 0.985074E-03 5 0.40 0.359254 0.358038 0.121595E-02 6 0.50 0.413540 0.412180 0.135997E-02 7 0.60 0.438703 0.437309 0.139455E-02 8 0.70 0.424186 0.422888 0.129771E-02 9 0.80 0.357134 0.356087 0.104777E-02 10 0.90 0.221987 0.221364 0.622818E-03 11 1.00 0.00000 0.00000 0.00000 L2 norm of error = 0.338872E-02 Seminorm of error = 0.138705 FEM1D_BVP_LINEAR_TEST05 A3(X) = 1.0 + X * X for X .le. 1/3 = 7/9 + X for 1/3 < X C1(X) = 0.0 F5(X) = ( X + 3 X^2 + 5 X^3 + X^4 ) * exp ( X ) for X .le. 1/3 = ( - 1 + 10/3 X + 43/9 X^2 + X^3 ) .* exp ( X ) for 1/3 .le. X U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 I X U Uexact Error 1 0.00 0.255351E-14 0.00000 0.255351E-14 2 0.10 0.999805E-01 0.994654E-01 0.515151E-03 3 0.20 0.196432 0.195424 0.100789E-02 4 0.30 0.284924 0.283470 0.145384E-02 5 0.40 0.359566 0.358038 0.152843E-02 6 0.50 0.413603 0.412180 0.142291E-02 7 0.60 0.438574 0.437309 0.126559E-02 8 0.70 0.423939 0.422888 0.105136E-02 9 0.80 0.356861 0.356087 0.774081E-03 10 0.90 0.221791 0.221364 0.426454E-03 11 1.00 0.00000 0.00000 0.00000 L2 norm of error = 0.349352E-02 Seminorm of error = 0.138709 FEM1D_BVP_LINEAR_TEST06 A1(X) = 1.0 C1(X) = 0.0 F6(X) = pi*pi*sin(pi*X) U4(X) = sin(pi*x) Compute L2 norm and seminorm of error for various N. N L2 error Seminorm error 11 0.005798 0.201186 21 0.001453 0.100697 41 0.000363 0.050361 81 0.000091 0.025182 161 0.000023 0.012591 FEM1D_BVP_LINEAR_PRB Normal end of execution. 19 February 2012 3:12:11.646 PM