1 October   2013   9:29:48.884 AM      
 
FEM1D_PMETHOD
  FORTRAN77 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 output points =   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   1.00000    
   0   1  0.208167E-16
   0   2 -0.624500E-16
 
   1   0  0.346945E-16
   1   1   1.00000    
   1   2  0.173472E-16
 
   2   0 -0.227682E-15
   2   1  0.379471E-16
   2   2   1.00000    
 
  Representation of solution:
 
  Basis function coefficients:
 
   0  0.954930    
   1 -0.125361E-17
   2 -0.220787    
 
 
       X     Approximate Solution
 
  -1.00000       0.00000    
 -0.800000      0.308802    
 -0.600000      0.588546    
 -0.400000      0.809559    
 -0.200000      0.950645    
   0.00000      0.999087    
  0.200000      0.950645    
  0.400000      0.809559    
  0.600000      0.588546    
  0.800000      0.308802    
   1.00000       0.00000    
 
 
  Comparison of computed and exact solutions:
 
    X        U computed    U exact     Error
 
  -1.000       0.000      0.6123E-16  0.6123E-16
 -0.8000      0.3088      0.3090      0.2149E-03
 -0.6000      0.5885      0.5878     -0.7612E-03
 -0.4000      0.8096      0.8090     -0.5423E-03
 -0.2000      0.9506      0.9511      0.4112E-03
   0.000      0.9991       1.000      0.9130E-03
  0.2000      0.9506      0.9511      0.4112E-03
  0.4000      0.8096      0.8090     -0.5423E-03
  0.6000      0.5885      0.5878     -0.7612E-03
  0.8000      0.3088      0.3090      0.2149E-03
   1.000       0.000      0.6123E-16  0.6123E-16
 
  Little L2 error =  0.173531E-02
 
 
FEM1D_PMETHOD
  Normal end of execution.
 
 1 October   2013   9:29:48.885 AM