clenshaw_curtis_rule


clenshaw_curtis_rule, a MATLAB 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 GNU LGPL 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:

alpert_rule, a MATLAB code which can set up an alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.

ccn_rule, a MATLAB code which defines a nested clenshaw curtis quadrature rule.

chebyshev1_rule, a MATLAB code which can compute and print a gauss-chebyshev type 1 quadrature rule.

chebyshev2_rule, a MATLAB code which can compute and print a gauss-chebyshev type 2 quadrature rule.

clenshaw_curtis_rule_test

gegenbauer_rule, a MATLAB code which can compute and print a gauss-gegenbauer quadrature rule.

gen_hermite_rule, a MATLAB code which can compute and print a generalized gauss-hermite quadrature rule.

gen_laguerre_rule, a MATLAB code which can compute and print a generalized gauss-laguerre quadrature rule.

hermite_rule, a MATLAB code which can compute and print a gauss-hermite quadrature rule.

jacobi_rule, a MATLAB code which can compute and print a gauss-jacobi quadrature rule.

laguerre_rule, a MATLAB code which can compute and print a gauss-laguerre quadrature rule.

legendre_rule, a MATLAB code which can compute and print a gauss-legendre quadrature rule.

line_felippa_rule, a MATLAB code which returns the points and weights of a felippa quadrature rule over the interior of a line segment in 1d.

patterson_rule, a MATLAB code which computes a gauss-patterson quadrature rule.

power_rule, a MATLAB code which constructs a power rule, that is, a product quadrature rule from identical 1d factor rules.

quadrature_rules_clenshaw_curtis, a dataset directory which contains quadrature rules for integration on [-1,+1], using a clenshaw curtis rule.

truncated_normal_rule, a MATLAB 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 16 December 2018.