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:

Robert Piessens,
Some Aspects of Gaussian Quadrature Formulas for
the Numerical Inversion of the Laplace Transform,
The Computer Journal,
November 1971, Volume 14, pages 433435.

Robert Piessens,
Algorithm 453: Gaussian Quadrature Formulas for
Bromwich's Integral,
Communications of the ACM,
August 1973, Volume 16, Number 8, pages 486487.
Related Data and Programs:
toms453_test
Source Code:
Last revised on 13 March 2021.