20 May 2014 11:11:14 AM

FILON_PRB
  C version
  Test the FILON library.

TEST01
  FILON_TAB_COS estimates the integral of.
  F(X) * COS ( T * X )
  Use integrands F(X)=1, X, X^2.

  A = 0
  B = 6.28319
  N = 11

       T                      Approximate             Exact

                       1              -1.90548e-16              -2.44929e-16
                       1              -1.32252e-15              -1.55431e-15
                       1                   12.5664                   12.5664

                       2              -2.59008e-16              -2.44929e-16
                       2               -1.4655e-15              -1.52656e-15
                       2                   3.14159                   3.14159

                      10              -2.79029e-16              -2.44929e-16
                      10              -1.53466e-15              -1.53877e-15
                      10                  0.125664                  0.125664

TEST02
  Integrate F(X) = log(1+X)*cos(T*X):
  Supply integrand as a table.
  T = 10, and N increases

       N    Approximate             Exact                   Error

    21               -0.00847842               -0.00844659              -3.18234e-05
    41               -0.00847842               -0.00844659              -3.18234e-05
    81               -0.00844826               -0.00844659              -1.67029e-06
   161               -0.00844669               -0.00844659              -9.94681e-08
   321                -0.0084466               -0.00844659              -6.14072e-09
   641               -0.00844659               -0.00844659               -3.8248e-10

TEST03
  Integrate F(X)=log(1+X)*cos(T*X):
  Supply integrand as a function.
  T = 10, and N increases

       N    Approximate             Exact                   Error

    21               -0.00847842               -0.00844659              -3.18234e-05
    41               -0.00847842               -0.00844659              -3.18234e-05
    81               -0.00844826               -0.00844659              -1.67029e-06
   161               -0.00844669               -0.00844659              -9.94681e-08
   321                -0.0084466               -0.00844659              -6.14072e-09
   641               -0.00844659               -0.00844659               -3.8248e-10

TEST04
  FILON_TAB_SIN estimates the integral of.
  F(X) * SIN ( T * X )
  Use integrands 1, X, X^2.

  A = 0
  B = 6.28319
  N = 11

       T                      Approximate             Exact


                       1               8.42591e-17                         0
                       1                  -6.28319                  -6.28319
                       1                  -39.4784                  -39.4784

                       2              -3.50982e-17                         0
                       2                  -3.14159                  -3.14159
                       2                  -19.7392                  -19.7392

                      10                6.1957e-32                         0
                      10                 -0.628319                 -0.628319
                      10                  -3.94784                  -3.94784

TEST05
  Integrate F(X)=log(1+X)*sin(T*X):
  Supply integrand as a table.
  T = 10, and N increases

       N    Approximate             Exact                   Error

    21                 -0.198557                 -0.197627              -0.000930023
    41                 -0.197628                 -0.197627              -1.40595e-06
    81                 -0.197627                 -0.197627               2.49144e-07
   161                 -0.197627                 -0.197627               1.91842e-08
   321                 -0.197627                 -0.197627               1.24997e-09
   641                 -0.197627                 -0.197627               7.89019e-11

TEST06
  Integrate F(X)=log(1+X)*sin(T*X):
  Supply integrand as a function.
  T = 10, and N increases

       N    Approximate             Exact                   Error

    21                 -0.198557                 -0.197627              -0.000930023
    41                 -0.197628                 -0.197627              -1.40595e-06
    81                 -0.197627                 -0.197627               2.49144e-07
   161                 -0.197627                 -0.197627               1.91842e-08
   321                 -0.197627                 -0.197627               1.24997e-09
   641                 -0.197627                 -0.197627               7.89019e-11

FILON_PRB
  Normal end of execution.

20 May 2014 11:11:14 AM