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An infinite element and a formula for numerical quadrature over an infinite interval
Author(s) -
Pissanetzky Sergio
Publication year - 1983
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620190611
Subject(s) - quadrature (astronomy) , mathematics , element (criminal law) , gauss–kronrod quadrature formula , orthonormal basis , tanh sinh quadrature , gaussian quadrature , laguerre polynomials , mathematical analysis , legendre polynomials , gauss–jacobi quadrature , numerical integration , interval (graph theory) , clenshaw–curtis quadrature , integral equation , nyström method , combinatorics , physics , quantum mechanics , political science , law , optics
In this publication we present a new infinite element and discuss a formula for numerical quadrature over infinite regions. Both the element and the formula are based on the properties of a set of orthonormal functions, obtained by mapping the Legendre polynomials on the infinite interval. The element can represent any (physical) function over the entire infinite region, and the formula can integrate most integrands over the infinite interval. They are thus very convenient for implementation in a general computer program, which could then be used to solve different problems with no restrictions concerning the asymptotic behaviour of the solutions or the form of integrands to be integrated over the infinite interval. However, the element and the formula will perform at their best when used in conjunction, and for problems of electrostatic, magnetostatic, etc., potential. The formula was compared with other existing formulae and found to be either superior or satisfactory in practically all cases, as shown by the results of many numerical experiments. Expressions of shape functions are given for the element. A test problem was solved using the element and the formula, and the results are shown to be more accurate than those obtained when solving the same problem using infinite elements with exponential decay and Gauss‐Laguerre numerical quadrature.