legendre_rule
legendre_rule,
a Fortran90 code which
generates a Gauss-Legendre quadrature rule,
based on user input.
The rule is written to three files for easy use as input
to other programs.
The Gauss-Legendre 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:
legendre_rule order a b filename
where
-
order is the number of points in the quadrature rule.
-
a is the left endpoint;
-
b is the right endpoint.
-
filename specifies the output filenames:
filename_w.txt,
filename_x.txt, and filename_r.txt,
containing the weights, abscissas, and interval limits.
Licensing:
The information on this web page is distributed under the MIT license.
Languages:
legendre_rule is available in
a C version and
a C++ version and
a Fortran90 version and
a MATLAB version and
an Octave version and
a Python version.
Related Data and Programs:
legendre_rule_test
f90_rule,
a Fortran90 code which
computes a quadrature rule which
estimates the integral of a function f(x), which might be defined over
a one dimensional region (a line) or more complex shapes such as
a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional
region, and which might include an associated weight function w(x).
Reference:
-
Milton Abramowitz, Irene Stegun,
Handbook of Mathematical Functions,
National Bureau of Standards, 1964,
ISBN: 0-486-61272-4,
LC: QA47.A34.
-
Philip Davis, Philip Rabinowitz,
Methods of Numerical Integration,
Second Edition,
Dover, 2007,
ISBN: 0486453391,
LC: QA299.3.D28.
-
Sylvan Elhay, Jaroslav Kautsky,
Algorithm 655:
IQPACK,
Fortran Subroutines for the Weights of Interpolatory Quadrature,
ACM Transactions on Mathematical Software,
Volume 13, Number 4, December 1987, pages 399-415.
-
Jaroslav Kautsky, Sylvan Elhay,
Calculation of the Weights of Interpolatory Quadratures,
Numerische Mathematik,
Volume 40, 1982, pages 407-422.
-
Roger Martin, James Wilkinson,
The Implicit QL Algorithm,
Numerische Mathematik,
Volume 12, Number 5, December 1968, pages 377-383.
-
Arthur Stroud, Don Secrest,
Gaussian Quadrature Formulas,
Prentice Hall, 1966,
LC: QA299.4G3S7.
Source Code:
Last revised on 26 July 2020.