A comparison of the error function and the tanh transformation as progressive rules for double and triple singular integrals
type: Item
instance of: scholarly article
title: A comparison of the error function and the tanh transformation as progressive rules for double and triple singular integrals
zbMATH Open document ID: 0708.65024
DOI: 10.1016/0377-0427(90)90023-S
author: V. U. Aihie
author: Gwynne Evans
published in: Journal of Computational and Applied Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Numerical integrations are performed over cubic regions in two and three dimensions on singular integrands using appropriate transformations onto the whole of \(\mathbb R^2\) or \(\mathbb R^3\) to enable truncated product trapezoidal, or trapezoidal and Clenshaw-Curtis rules [\textit{C. W. Clenshaw} and \textit{A. R. Curtis}, Numer. Math. 2, 197--205 (1960; Zbl 0093.14006)] to be employed effectively. Transformations of the form \(x=\tanh (g(t))\) with \(g(t)=t^n\) or \(g(t)=c \sinh (t)\) (double exponential DE), as well as the more complicated error function type are used. There are tables of interesting illustrative examples resulting from significant computation. Both end-point and non end-point singularities are considered in two and in three dimensions. The non end-point singularities are handled by splitting the integrals into sums of end-point type integrals which are separately scaled to \([-1,1]\) before transformation. The different transformations and rules are compared. In the three- dimensional case comparisons are also made with a method of \textit{M. Sugihara} [J. Comput. Appl. Math. 17, 197--213 (1977; Zbl 0639.65014)] which in a particular sense approaches optimality.
reviewed by: William E. Smith
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 30E20
zbMATH DE Number: 4164014
zbMATH Keywords: error function
zbMATH Keywords: tanh transformation
zbMATH Keywords: singular double integrals
zbMATH Keywords: singular triple integrals
zbMATH Keywords: double exponential transformation
zbMATH Keywords: Clenshaw-Curtis rules
zbMATH Keywords: end-point singularities
MaRDI profile type: Publication
cites work: The tanh transformation for double integrals with singularities - a progressive rule
cites work: Q5533688
cites work: The tanh transformation for singular integrals
cites work: An IMT-type double exponential formula for numerical integration
cites work: Quadrature formulas obtained by variable transformation and the DE-rule
cites work: Method of good matrices for multi-dimensional numerical integrations - An extension of the method of good lattice points
cites work: Quadrature formulas obtained by variable transformation
full work available at URL: 0377-0427(90)90023-s
OpenAlex ID: W1988058699
description: scientific article; zbMATH DE number 4164014