Programs in Physics & Physical Chemistry
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|Manuscript Title: GISP: Gauss-integration subroutine pack.|
|Authors: M. Rysavy|
|Program title: GISP|
|Catalogue identifier: AAPE_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 32(1984)191|
|Programming language: Fortran.|
|Computer: ES 1040.|
|Operating system: OS/21.8F - MVT.|
|RAM: 48K words|
|Word size: 8|
|Keywords: General purpose, Numerical, Quadrature, Orthogonal polynomials, Gauss method.|
Nature of problem:
A calculation of definite integrals appears in almost all physical problems. In many cases the integrals have to be evaluated numerically. The present pack enables one to employ the Gauss integration method with an optional number of nodes for four different weight functions, i.e. for four different types of integrals.
The integration may be based on the Legendre, Jacobi, Hermite, or Laguerre polynomials. The nodes of the required polynomial are roughly found by a direct scan of a suitable interval (which is automatically chosen by the program) and then corrected by the interval-halving method. The corresponding Gaussian weights are determined and the integral is evaluated. Since the determination of the nodes and weights is time-consuming, the program provides the possibility to skip their evaluation if they are already known (e.g. from the previous call).
In principle, there are no restrictions, but the program was tested up to 250 nodes only.
The running time depends on several factors and more detailed information is provided in the sect. 7 of the long write-up. The test run took about 5.5 min.
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