toms351

toms351, a FORTRAN77 code which implements ACM toms algorithm 351, for modified Romberg quadrature.

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.

Usage:

call romint ( val, err, eps, a, b, n, maxe, f )
where VAL is returned as the estimated integral, ERR is returned as an error bound for the estimated integral, EPS is the desired accuracy, A and B define the interval of integration, N is the number of function evaluations, MAXE is the number of extrapolations, and F is the name of the FORTRAN function that evaluates the integrand.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

toms351 is available in a FORTRAN77 version.

Related Data and Programs:

toms351_test

intlib, a FORTRAN90 library which can estimate the integral of a function.

QUADPACK, a FORTRAN90 library which can estimate the integral of a function, including weight functions, singularities, and infinite intervals.

QUADRULE, a FORTRAN90 library which defines many simple quadrature schemes.

STROUD, a FORTRAN90 library which defines quadrature schemes for a number of geometrically interesting regions.

TEST_INT, a FORTRAN90 library which contains routines which define integrands suitable for testing integration software.

toms468, a FORTRAN77 library which carries out the automatic integration of a function.

Reference:

  1. ND Cook,
    Remark on Algorithm 351: Modified Romberg Quadrature,
    Communications of the ACM,
    April 1970, Volume 13, Issue 4, page 263.
  2. Graeme Fairweather,
    Algorithm 351: Modified Romberg Quadrature,
    Communications of the ACM,
    June 1969, Volume 12, page 324.
  3. George Wallick,
    Remark on Algorithm 351: Modified Romberg Quadrature,
    Communications of the ACM,
    June 1970, Volume 13, Issue 6, page 374-376.

Source Code:

Last revised on 09 November 2023.