18 June 2014 11:11:01.755 AM FEM1D_BVP_LINEAR_PRB FORTRAN77 version Test the FEM1D_BVP_LINEAR library. 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 0.00000 0.00000 0.00000 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 l1 norm of error = 0.293988E-05 L2 norm of error = 0.400665E-02 Seminorm of error = 0.138667 TEST02 A2(X) = 1.0 C2(X) = 2.0 F2(X) = X * ( 5 - X ) * exp ( X ) U2(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 I X U Uexact Error 1 0.00 0.00000 0.00000 0.00000 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 l1 norm of error = 0.389237E-02 L2 norm of error = 0.369835E-02 Seminorm of error = 0.138675 TEST03 A3(X) = 1.0 C3(X) = 2.0 * X F3(X) = - X * ( 2 * X * X - 3 * X - 3 ) * exp ( X ) U3(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 I X U Uexact Error 1 0.00 0.00000 0.00000 0.00000 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 l1 norm of error = 0.272633E-02 L2 norm of error = 0.377892E-02 Seminorm of error = 0.138671 TEST04 A4(X) = 1.0 + X * X C4(X) = 0.0 F4(X) = ( X + 3 X^2 + 5 X^3 + X^4 ) * exp ( X ) U4(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 I X U Uexact Error 1 0.00 0.00000 0.00000 0.00000 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 l1 norm of error = 0.896908E-02 L2 norm of error = 0.338872E-02 Seminorm of error = 0.138705 TEST05 A5(X) = 1.0 + X * X for X .le. 1/3 = 7/9 + X for 1/3 < X C5(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 U5(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 I X U Uexact Error 1 0.00 0.00000 0.00000 0.00000 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 l1 norm of error = 0.944571E-02 L2 norm of error = 0.349352E-02 Seminorm of error = 0.138709 TEST06 A6(X) = 1.0 C6(X) = 0.0 F6(X) = pi*pi*sin(pi*X) U6(X) = sin(pi*x) Compute L2 norm and seminorm of error for various N. N L1 error L2 error Seminorm error 11 0.000043 0.005798 0.201186 21 0.000005 0.001453 0.100697 41 0.000001 0.000363 0.050361 81 0.000000 0.000091 0.025182 161 0.000000 0.000023 0.012591 TEST07 Becker/Carey/Oden example Compute L2 norm and seminorm of error for various N. N L1 error L2 error Seminorm error 11 0.115758 0.054894 2.119623 21 0.098462 0.015170 1.069906 41 0.049593 0.004950 0.685573 81 0.024515 0.001267 0.350963 161 0.012093 0.000317 0.176055 TEST08 Solve -( A(x) U'(x) )' + C(x) U(x) = F(x) for 0 < x < 1, with U(0) = U(1) = 0. A8(X) = 1.0 C8(X) = 0.0 F8(X) = X * ( X + 3 ) * exp ( X ), X .le. 2/3 = 2 * exp ( 2/3), 2/3 < X U8(X) = X * ( 1 - X ) * exp ( X ), X .le. 2/3 = X * ( 1 - X ) * exp ( 2/3 ), 2/3 < X Number of nodes = 11 I X U Uexact Error 1 0.00 0.00000 0.00000 0.00000 2 0.10 0.845329E-01 0.994654E-01 0.149325E-01 3 0.20 0.165559 0.195424 0.298650E-01 4 0.30 0.238673 0.283470 0.447975E-01 5 0.40 0.298308 0.358038 0.597300E-01 6 0.50 0.337518 0.412180 0.746626E-01 7 0.60 0.347713 0.437309 0.895952E-01 8 0.70 0.319447 0.409024 0.895770E-01 9 0.80 0.251919 0.311637 0.597180E-01 10 0.90 0.145437 0.175296 0.298590E-01 11 1.00 0.00000 0.00000 0.00000 l1 norm of error = 0.492737 L2 norm of error = 0.595979E-01 Seminorm of error = 0.240692 TEST09 Solve -( A(x) U'(x) )' + C(x) U(x) = F(x) for 0 < x < 1, with U(0) = U(1) = 0. A8(X) = 1.0 C8(X) = 0.0 F9(X) = X * ( X + 3 ) * exp ( X ), X .le. 2/3 = 2 * exp ( 2/3), 2/3 < X U9(X) = X * ( 1 - X ) * exp ( X ), X .le. 2/3 = X * ( 1 - X ), 2/3 < X Number of nodes = 11 I X U Uexact Error 1 0.00 0.00000 0.00000 0.00000 2 0.10 0.729598E-01 0.994654E-01 0.265056E-01 3 0.20 0.142413 0.195424 0.530111E-01 4 0.30 0.203954 0.283470 0.795167E-01 5 0.40 0.252016 0.358038 0.106022 6 0.50 0.279652 0.412180 0.132528 7 0.60 0.278275 0.437309 0.159034 8 0.70 0.240438 0.210000 0.304383E-01 9 0.80 0.180292 0.160000 0.202922E-01 10 0.90 0.100146 0.900000E-01 0.101461E-01 11 1.00 0.00000 0.00000 0.00000 l1 norm of error = 0.617494 L2 norm of error = 0.822364E-01 Seminorm of error = 0.233968 FEM1D_BVP_LINEAR_PRB Normal end of execution. 18 June 2014 11:11:01.785 AM