jacobi_rule

jacobi_rule, an Octave code which generates a specific Gauss-Jacobi quadrature rule, based on user input.

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

The Gauss-Jacobi quadrature rule is used as follows:

        Integral ( A <= x <= B ) (B-x)^alpha (x-A)^beta f(x) dx

is to be approximated by

        Sum ( 1 <= i <= order ) w(i) * f(x(i))

a b

jacobi_rule ( order, alpha, beta, a, b, 'filename' )

where

order is the number of points in the quadrature rule.
alpha is the exponent of (B-x), which must be greater than -1.
beta is the exponent of (x-A), which must be greater than -1.
a is the left endpoint;
b is the right endpoint.
'filename' specifies how the rule is to be reported: filename_w.txt, filename_x.txt, and filename_r.txt, containing the weights, abscissas, and interval limits.

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

jacobi_rule is available in a C++ version and a FORTRAN90 version and a MATLAB version and an Octave version.

jacobi_polynomial, a MATLAB code which evaluates the Jacobi polynomial and associated functions.

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Volume 40, 1982, pages 407-422.
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Last revised on 25 September 2022.