01 October 2013 08:33:31 AM

FEM1D_PMETHOD
  C++ version

  Solve the two-point boundary value problem

  - d/dX (P dU/dX) + Q U  =  F

  on the interval [-1,1], with
  U(-1) = U(1) = 0.

  The P method is used, which represents U as
  a weighted sum of orthogonal polynomials.


  Highest degree polynomial to use is 2
  Number of points to be used for output = 10

  Problem #2:
  U=cos(0.5*pi*x),
  P=1,
  Q=0,
  F=0.25*pi*pi*cos(0.5*pi*x)

  Basis function orthogonality test:

   i   j     b(i,j)/a(i)


       0       0             1
       0       1   2.08167e-17
       0       2  -8.32667e-17

       1       0   3.46945e-17
       1       1             1
       1       2   1.73472e-17

       2       0  -3.03577e-16
       2       1   3.79471e-17
       2       2             1

  Representation of solution:

  Basis function coefficients:

         0       0.95493
         1  -1.25361e-18
         2     -0.220787


       X     Approximate Solution

            -1             0
          -0.8      0.308802
          -0.6      0.588546
          -0.4      0.809559
          -0.2      0.950645
             0      0.999087
           0.2      0.950645
           0.4      0.809559
           0.6      0.588546
           0.8      0.308802
             1             0


  Comparison of computed and exact solutions:

    X        U computed    U exact     Difference

        -1             0   6.12323e-17   6.12323e-17
      -0.8      0.308802      0.309017   0.000214907
      -0.6      0.588546      0.587785  -0.000761186
      -0.4      0.809559      0.809017  -0.000542347
      -0.2      0.950645      0.951057    0.00041123
         0      0.999087             1   0.000913031
       0.2      0.950645      0.951057    0.00041123
       0.4      0.809559      0.809017  -0.000542347
       0.6      0.588546      0.587785  -0.000761186
       0.8      0.308802      0.309017   0.000214907
         1             0   6.12323e-17   6.12323e-17

  Big L2 error = 0.000572595

PMETHOD
  Normal end of execution.

01 October 2013 08:33:31 AM