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The tanh transformation for the solution of singular integral equations
Author(s) -
Tsamasphyros G.,
Androulidakis P.
Publication year - 1987
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.1620240306
Subject(s) - mathematics , gravitational singularity , quadrature (astronomy) , regular singular point , singular integral , mathematical analysis , hyperbolic function , singular solution , singular point of a curve , transformation (genetics) , integral equation , physics , biochemistry , chemistry , optics , gene
Using a tanh transformation a quadrature formula for the evaluation of singular integrals is obtained. The formula has the same step length h as the formula for regular integrals derived by F. Stenger. These quadrature formulae are valid for end point singularities of any order and their error exhibits an exponential decay when the number of integrations tends to infinity. Using these formulae the solution of singular integral equations does not depend on the order of the end point singularities. Furthermore the collocation points are given by a very simple equation and, in the case of constant coefficients, by a closed‐form formula.

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