Abscissae and weights for the Gauss-Laguerre quadrature formula

2019-12-06T07:31:14Z (GMT) by Tadashi Takemasa
Abstract A program is described which calculates the abscissae and weights for the Gauss-Laguerre quadrature formula for integrals of the form ∫∈e^(-x)x^α f(x)dx very rapidly and with high accuracy even in the case of many abscissae. The abscissae are given by the zeros of the Laguerre polynomials, which are found by the Newton-Raphson method with suitable initial approximations. The program is useful for the problem in the case of an integrand f(x) oscillating rapidly. Title of program: GAUSSLA Catalogue Id: ABFJ_v1_0 Nature of problem In the study of physical problems, the need often arises for evaluating definite intergrals numerically. The Gaussian quadrature is known as one of the most efficient quadrature schemes. The present program generates the abscissae and weights for the Gauss-Laguerre quadrature formula for integrals very rapidly and with high accuracy even in the case of a great many abscissae. Versions of this program held in the CPC repository in Mendeley Data ABFJ_v1_0; GAUSSLA; 10.1016/0010-4655(88)90178-6 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)