TOMS418
Filon Quadrature

TOMS418 is a FORTRAN77 library which estimates Fourier integrals of the form integral ( a<=x<=b ) f(x) * cos(wx) dx, or integral ( a<=x<=b ) f(x) * sin(wx) dx, by Bo Einarsson. This is a version of ACM TOMS algorithm 418.

While the text of many ACM TOMS algorithms is available online through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html, most of the early algorithms are not available. This is one of them. I typed it in.

Usage:

call fspl2 ( f, a, b, fpa, fpb, fba, fbb, w, eps, max, lc, ls, c, s )

estimates the integral of F(X)*COS(W*X) and F(X)*SIN(W*X).

Languages:

TOMS418 is available in a FORTRAN77 version.

Related Programs:

INTLIB, a FORTRAN90 library which includes routines to do Filon quadrature.

TOMS353, a FORTRAN77 library which estimates an integral of the form integral ( a <= x <= b ) f(x) cos(w*x) dx or integral ( a <= x <= b ) f(x) sin(w*x) dx using Filon quadrature, by Chase and Fosdick. This is a version of ACM TOMS algorithm 353.

Author:

Bo Einarsson

Reference:

1. Bo Einarsson,
   Algorithm 418: Calculation of Fourier Integrals,
   Communications of the ACM,
   Volume 15, Number 1, January 1972, pages 47-48.

Source Code:

• toms418.f, the source code.
• toms418.sh, commands to compile the source code.

Examples and Tests:

• toms418_prb.f, a sample calling program.
• toms418_prb.sh, commands to compile and run the sample program.
• toms418_prb_output.txt, the output file.

List of Routines:

• FSPL2 carries out the Filon quadrature.
• ENDT2 performs Richardson extrapolation.

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