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International Journal of Mathematics and Mathematical Sciences
Volume 4, Issue 4, Pages 775-794
http://dx.doi.org/10.1155/S0161171281000604

Fast methods for the solution of singular integro-differential and differential equations

Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

Received 3 July 1979

Copyright © 1981 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Uniform methods based on the use of the Galerkin method and different Chebyshev expansion sets are developed for the numerical solution of linear integrodifferential equations of the first order. These methods take a total solution time 0(N2lnN) using N expansion functions, and also provide error extimates which are cheap to compute. These methods solve both singular and regular integro-differential equations. The methods are also used in solving differential equations.