QUADRULE
Functions for Computing Quadrature Rules

QUADRULE is a collection of Mathematica scripts which can be used to compute and print certain simple quadrature rules.

Mathematica has built-in functions for Newton-Cotes and Gauss-Legendre rules. It can also be coaxed into computing Hermite and Laguerre quadrature rules. The scripts given here present the results in a form suitable for copying into a program in C, FORTRAN or MATLAB.

Values computed by these scripts were, in some cases, used to define quadrature lookup values in the C, C++, FORTRAN90 and MATLAB "QUADRULE" libraries.

Licensing:

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

Languages:

QUADRULE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATHEMATICA version and a MATLAB version.

Related Data and Programs:

ARBITRARY_WEIGHT_RULE, a MATHEMATICA program which accepts a formula for an arbitrary (but nonnegative) weight function over an interval, and determines the points and weights of a corresponding Gaussian quadrature rule, by Fukuda, Katsuya, Alt and Matveenko.

NEWTON_COTES is a MATHEMATICA library which computes the points and weights for Newton-Cotes quadrature.

QUADRATURE_WEIGHTS a FORTRAN90 library which illustrates techniques for computing the weights of a quadrature rule, assuming that the points have been specified.

TOMS655 a C library which computes the weights for interpolatory quadrature rules;
this library is commonly called IQPACK;
this is a C version of ACM TOMS algorithm 655.

Reference:

1. Milton Abramowitz, Irene Stegun,
   Handbook of Mathematical Functions,
   National Bureau of Standards, 1964,
   ISBN: 0-486-61272-4,
   LC: QA47.A34.
2. Vladimir Krylov,
   Approximate Calculation of Integrals,
   Dover, 2006,
   ISBN: 0486445798,
   LC: QA311.K713.
3. Arthur Stroud, Don Secrest,
   Gaussian Quadrature Formulas,
   Prentice Hall, 1966,
   LC: QA299.4G3S7.
4. Stephen Wolfram,
   The Mathematica Book,
   Fourth Edition,
   Cambridge University Press, 1999,
   ISBN: 0-521-64314-7,
   LC: QA76.95.W65.

Source Code:

• gen_laguerre_set.nb, computes a generalized Laguerre quadrature rule.
• hermite_set.nb, computes a Hermite quadrature rule.
• laguerre_set.nb, computes a Laguerre quadrature rule.
• legendre_set.nb, computes a Legendre quadrature rule.
• ncc_set.nb, computes a Newton-Cotes closed quadrature rule.
• ncoh_set.nb, computes a Newton-Cotes "open half" quadrature rule.

You can go up one level to the Mathematica packages and notebooks.