FILON
Quadrature for Oscillatory Integrands

FILON is a FORTRAN77 library which can approximate integrals in which the integrand includes an oscillatory factor of sin(k*x) or cos(k*x).

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

FILON is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

QUADRULE, a FORTRAN77 library which defines quadrature rules for 1D domains.

TOMS353, a FORTRAN77 library which estimates an integral involving a cosine or sine factor using Filon quadrature; this is a version of ACM TOMS algorithm 353.

TOMS418, a FORTRAN77 library which estimates the integral of a function with a sine or cosine factor. This is a version of ACM TOMS algorithm 418.

TOMS427, a FORTRAN77 library which estimates a Fourier cosine integral; this is a version of ACM TOMS algorithm 427.

Reference:

1. Stephen Chase, Lloyd Fosdick,
   An Algorithm for Filon Quadrature,
   Communications of the Association for Computing Machinery,
   Volume 12, Number 8, August 1969, pages 453-457.
2. Stephen Chase, Lloyd Fosdick,
   Algorithm 353: Filon Quadrature,
   Communications of the Association for Computing Machinery,
   Volume 12, Number 8, August 1969, pages 457-458.
3. Bo Einarsson,
   Algorithm 418: Calculation of Fourier Integrals,
   Communications of the ACM,
   Volume 15, Number 1, January 1972, pages 47-48.

Source Code:

• filon.f, the source code.
• filon.sh, BASH commands to compile the source code.

Examples and Tests:

• filon_prb.f, a sample calling program.
• filon_prb.sh, BASH commands to compile and run the sample program.
• filon_prb_output.txt, the output file.

List of Routines:

• FILON_FUN_COS uses Filon's method on integrals with a cosine factor.
• FILON_TAB_COS uses Filon's method on integrals with a cosine factor.
• FILON_FUN_SIN uses Filon's method on integrals with a sine factor.
• FILON_TAB_SIN uses Filon's method on integrals with a sine factor.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.