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A numerical solution of singular integral equations without using special collocation points
Author(s) -
Tsamasphyros G.,
Theocaris P. S.,
Stassinakis C. A.
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.1620190309
Subject(s) - mathematics , collocation method , collocation (remote sensing) , integral equation , discretization , singular integral , regular singular point , mathematical analysis , orthogonal collocation , singular solution , polynomial , function (biology) , differential equation , ordinary differential equation , computer science , machine learning , evolutionary biology , biology
A new technique for the solution of singular integral equations is proposed, where the unknown function may have a particular singular behaviour, different from the one defined by the dominant part of the singular integral equation. In this case the integral equation may be discretized by two different quadratures defined in such a way that the collocation points of the one correspond to the integration points of the other. In this manner the system is reduced to a n × n system of discrete equations and the method preserves, for the same number of equations, the same polynomial accuracy. The main advantage of the method is that it can proceed without using special collocation points. This new technique was tested in a series of typical examples and yielded results which are in good agreement with already existing solutions.