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Numerical solution of integral equations with a logarithmic kernel by the method of arbitrary collocation points
Author(s) -
Chrysakis A. C.,
Tsamasphyros G.
Publication year - 1992
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.1620330110
Subject(s) - gaussian quadrature , mathematics , logarithm , nyström method , quadrature (astronomy) , mathematical analysis , collocation (remote sensing) , collocation method , gauss–kronrod quadrature formula , polynomial , integral equation , numerical integration , kernel (algebra) , numerical analysis , singularity , gaussian , differential equation , pure mathematics , physics , computer science , ordinary differential equation , machine learning , optics , quantum mechanics
Abstract An integral equation whose kernel presents logarithmic singularity is numerically solved by the method of arbitrary collocation points (ACP). As a first step a Gaussian quadrature of order n (hence of polynomial accuracy 2 n − 1) is employed for the numerical approximation of the integral. Until now the collocation, which follows, was performed on special points x̄ k , determined as roots of appropriate transcedental functions, in order to retain the 2 n − 1 degree of polynomial accuracy of the Gaussian quadrature. In this paper an appropriate interpolatory technique is proposed, so that x k may be arbitrary and yet the high (2 n − 1) accuracy of the Gaussian quadrature is retained.