07-Jan-2022 19:59:50

fem1d_pmethod_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test fem1d_pmethod().
07-Jan-2022 19:59:50

FEM1D_PMETHOD
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2

  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      1.000000
     0     1      0.000000
     0     2     -0.000000

     1     0      0.000000
     1     1      1.000000
     1     2      0.000000

     2     0     -0.000000
     2     1      0.000000
     2     2      1.000000

  Representation of solution:

  Basis function coefficients:

     0      0.954930
     1     -0.000000
     2     -0.220787


       X     Approximate Solution

     -1.000000      0.000000
     -0.800000      0.308802
     -0.600000      0.588546
     -0.400000      0.809559
     -0.200000      0.950645
      0.000000      0.999087
      0.200000      0.950645
      0.400000      0.809559
      0.600000      0.588546
      0.800000      0.308802
      1.000000      0.000000


  Comparison of computed and exact solutions:

    X        U computed    U exact     Difference

  -1.000000      0.000000      0.000000      0.000000
  -0.800000      0.308802      0.309017      0.000215
  -0.600000      0.588546      0.587785     -0.000761
  -0.400000      0.809559      0.809017     -0.000542
  -0.200000      0.950645      0.951057      0.000411
  0.000000      0.999087      1.000000      0.000913
  0.200000      0.950645      0.951057      0.000411
  0.400000      0.809559      0.809017     -0.000542
  0.600000      0.588546      0.587785     -0.000761
  0.800000      0.308802      0.309017      0.000215
  1.000000      0.000000      0.000000      0.000000

  Big L2 error = 0.000573

FEM1D_PMETHOD
  Normal end of execution.

07-Jan-2022 19:59:50

fem1d_pmethod_test():
  Normal end of execution.

07-Jan-2022 19:59:50