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: https://www.acm.org/pubs/calgo or NETLIB: https://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 information on this web page is distributed under the MIT license.

Languages:

toms351 is available in a Fortran77 version.

Related Data and Programs:

toms351_test

intlib, a Fortran90 code which estimates the integral of a function.

quadpack, a Fortran90 library which can estimate the integral of a function, including weight functions, singularities, and infinite intervals.

quad_rule, a Fortran90 library which defines many simple quadrature schemes.

stroud_rule, a Fortran90 code 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.