03 March 2020 11:36:01 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  -3.90313e-16
       2       1   4.87891e-17
       2       2       1.28571

  Representation of solution:

  Basis function coefficients:

         0       0.95493
         1  -1.25361e-18
         2     -0.283868


       X     Approximate Solution

            -1             0
          -0.8       0.29881
          -0.6      0.582087
          -0.4      0.811679
          -0.2      0.960335
             0        1.0117
           0.2      0.960335
           0.4      0.811679
           0.6      0.582087
           0.8       0.29881
             1             0


  Comparison of computed and exact solutions:

    X        U computed    U exact     Difference

        -1             0   6.12323e-17   6.12323e-17
      -0.8       0.29881      0.309017     0.0102071
      -0.6      0.582087      0.587785     0.0056984
      -0.4      0.811679      0.809017    -0.0026619
      -0.2      0.960335      0.951057   -0.00927815
         0        1.0117             1    -0.0117033
       0.2      0.960335      0.951057   -0.00927815
       0.4      0.811679      0.809017    -0.0026619
       0.6      0.582087      0.587785     0.0056984
       0.8       0.29881      0.309017     0.0102071
         1             0   6.12323e-17   6.12323e-17

  Big L2 error = 0.00779738

FEM1D_PMETHOD
  Normal end of execution.

03 March 2020 11:36:01 AM