Paper Info
Title
An Extended Sigmoidal Transformation Technique for Evaluating Weakly Singular Integrals without Splitting the Integration Interval
Abstract
In this paper, we present an efficient transformation technique for accurate numerical evaluation of weakly singular integrals with interior singularities. The present transformation technique does not require any division of the integration interval. It is composed of two parts of a sigmoidal transformation whose tails coincide with a singular point smoothly up to the order of the sigmoidal transformation employed. Therefore, in using the standard Gauss quadrature rule, the present transformation has a feature in which the integration points are clustered into the interior singular point very closely, as in the case of endpoint singular integrals.The results of some numerical examples show the superiority of the present method over the existing methods.
Year
DOI
Venue
2003
10.1137/S1064827502414606
SIAM J. Scientific Computing
Keywords
Field
DocType
weakly singular integral,sigmoidal transformation,polynomial transformation,Gauss-Legendre quadrature rule
Singular point of a curve,Mathematical optimization,Polynomial transformation,Singular integral,Mathematical analysis,Numerical integration,Singular solution,Gravitational singularity,Gaussian quadrature,Mathematics,Sigmoid function
Journal
Volume
Issue
ISSN
25
1
1064-8275
Citations 
PageRank 
References 
2
0.68
1
Authors
1
Name
Order
Citations
PageRank
Beong In Yun18612.55