ROMBERG
Integral Estimation using Repeated Quadrature and Extrapolation
ROMBERG
is a FORTRAN90 library which
estimates the integral of a function f(x) over an interval [a,b]
using one of:

the trapezoidal rule;

the composite trapezoidal rule;

a sequence of composite trapezoidal rules;

a sequence of composite trapezoidal rules and Romberg extrapolation.
Licensing:
The computer code and data files described and made available on this
web page are distributed under
the GNU LGPL license.
Languages:
ROMBERG is available in
a FORTRAN90 version.
Related Data and Programs:
CLENSHAW_CURTIS_RULE,
a FORTRAN90 program which
defines a Clenshaw Curtis quadrature rule.
INTLIB,
a FORTRAN90 library which
contains a variety
of routines for numerical estimation of integrals in 1D.
QUADPACK,
a FORTRAN90 library which
contains a variety of routines for
numerical estimation of integrals in 1D.
QUADRULE,
a FORTRAN90 library which
defines quadrature rules for 1D domains.
Reference:

Philip Davis, Philip Rabinowitz,
Methods of Numerical Integration,
Second Edition,
Dover, 2007,
ISBN: 0486453391,
LC: QA299.3.D28.
Source Code:
Examples and Tests:
List of Routines:

ROMBERG_TRAP approximates an integral by extrapolating the trapezoidal rule.

TIMESTAMP prints the current YMDHMS date as a time stamp.

TRAPEZOID carries out the composite trapezoid rule.

TRAPEZOID_REFINE carries out a step of trapezoidal refinement.

TRAPEZOID_TOL repeatedly refines the trapezoid rule til a tolerance is met.
You can go up one level to
the FORTRAN90 source codes.
Last revised on 28 February 2013.