TOMS453
Gaussian Quadrature Formulas for Bromwich's Integral


TOMS453 is a FORTRAN90 library which implements ACM TOMS algorithm 453, which computes the abscissas and weights of a Gaussian quadrature formula of given order for Bromwich's integral.

The Bromwich integral is the inverse of the Laplace transform.

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 bromin ( n, s, tol, xr, xi, wr, wi, eps, ier )
      
N
the order of the rule;
S
the parameter in the integral;
TOL
an error tolerance;
XR, XI
the real and imaginary parts of the abscissas;
WR, WI
the real and imaginary parts of the weights;
EPS
the relatve accuracy estimate;
IER
the error flag.

Languages:

TOMS453 is available in a FORTRAN77 version and a FORTRAN90 version.

Reference:

  1. Robert Piessens,
    Some Aspects of Gaussian Quadrature Formulas for the Numerical Inversion of the Laplace Transform,
    The Computer Journal,
    November 1971, Volume 14, pages 433-435.
  2. Robert Piessens,
    Algorithm 453: Gaussian Quadrature Formulas for Bromwich's Integral,
    Communications of the ACM,
    August 1973, Volume 16, Number 8, pages 486-487.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.


Last revised on 12 July 2008.