Numerical solution for the weakly singular Fredholm integro-differential equations using Legendre multiwavelets

Authors:
Mehrdad Lakestani;Behzad Nemati Saray;Mehdi Dehghan
Affiliations:
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran;Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424 Hafez Avenue, Tehran, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

An effective method based upon Legendre multiwavelets is proposed for the solution of Fredholm weakly singular integro-differential equations. The properties of Legendre multiwavelets are first given and their operational matrices of integral are constructed. These wavelets are utilized to reduce the solution of the given integro-differential equation to the solution of a sparse linear system of algebraic equations. In order to save memory requirement and computational time, a threshold procedure is applied to obtain the solution to this system of algebraic equations. Through numerical examples, performance of the present method is investigated concerning the convergence and the sparseness of the resulted matrix equation.