filon_rule

filon_rule, a FORTRAN77 code which uses Filon's method to approximate integrals including 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_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

filon_rule_test

quad_rule, 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_rule 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_rule 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_rule 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_rule.f, the source code.
• filon_rule.sh, compiles the source code.