clenshaw_curtis_rule


clenshaw_curtis_rule, a C++ code which generates a Clenshaw Curtis quadrature rule based on user input.

The rule is written to three files for easy use as input to other programs.

The standard Clenshaw Curtis quadrature rule is used as follows:

        Integral ( A <= x <= B ) f(x) dx
      
is to be approximated by
        Sum ( 1 <= i <= order ) w(i) * f(x(i))
      

Usage:

clenshaw_curtis_rule order a b filename
where

Licensing:

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

Languages:

clenshaw_curtis_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CCN_RULE, a C++ code which defines a nested Clenshaw Curtis quadrature rule.

CHEBYSHEV1_RULE, a C++ code which can compute and print a Gauss-Chebyshev type 1 quadrature rule.

CHEBYSHEV2_RULE, a C++ code which can compute and print a Gauss-Chebyshev type 2 quadrature rule.

clenshaw_curtis_rule_test

GEGENBAUER_RULE, a C++ code which can compute and print a Gauss-Gegenbauer quadrature rule.

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HERMITE_RULE, a C++ code which can compute and print a Gauss-Hermite quadrature rule.

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LINE_NCC_RULE, a C++ code which computes a Newton Cotes Closed (NCC) quadrature rule for the line, that is, for an interval of the form [A,B], using equally spaced points which include the endpoints.

LINE_NCO_RULE, a C++ code which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.

PATTERSON_RULE, a C++ code which computes a Gauss-Patterson quadrature rule.

QUADRATURE_RULES_CLENSHAW_CURTIS, a dataset directory which contains quadrature rules for integration on [-1,+1], using a Clenshaw Curtis rule.

QUADRULE, a C++ code which defines 1-dimensional quadrature rules.

TRUNCATED_NORMAL_RULE, a C++ code which computes a quadrature rule for a normal probability density function (PDF), also called a Gaussian distribution, that has been truncated to [A,+oo), (-oo,B] or [A,B].

Reference:

  1. Milton Abramowitz, Irene Stegun,
    Handbook of Mathematical Functions,
    National Bureau of Standards, 1964,
    ISBN: 0-486-61272-4,
    LC: QA47.A34.
  2. Philip Davis, Philip Rabinowitz,
    Methods of Numerical Integration,
    Second Edition,
    Dover, 2007,
    ISBN: 0486453391,
    LC: QA299.3.D28.
  3. Arthur Stroud, Don Secrest,
    Gaussian Quadrature Formulas,
    Prentice Hall, 1966,
    LC: QA299.4G3S7.

Source Code:


Last revised on 20 February 2020.