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:

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.
Source Code:
Examples and Tests:
List of Routines:

BROMIN computes the abscissas and weights for
a Gaussian quadrature formula for Bromwich's integral.

DGAMMA calculates the gamma function for a real argument X.

TIMESTAMP prints out the current YMDHMS date as a timestamp.
You can go up one level to
the FORTRAN90 source codes.
Last revised on 12 July 2008.