toms453

toms453, a FORTRAN90 code 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.

The text of many ACM TOMS algorithms is available online through ACM: https://calgo.acm.org/ or NETLIB: https://www.netlib.org/toms/index.html.

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.

Licensing:

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

Languages:

toms453 is available in 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.

Related Data and Programs:

toms453_test

Source Code:

• toms453.f90, the source code.
• toms453.sh, compiles the source code.