Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients

Authors:
Abbas Saadatmandi;Mehdi Dehghan
Affiliations:
Department of Mathematics, Faculty of Science, University of Kashan, Kashan, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

The main aim of this paper is to apply the Legendre polynomials for the solution of the linear Fredholm integro-differential-difference equation of high order. This equation is usually difficult to solve analytically. Our approach consists of reducing the problem to a set of linear equations by expanding the approximate solution in terms of shifted Legendre polynomials with unknown coefficients. The operational matrices of delay and derivative together with the tau method are then utilized to evaluate the unknown coefficients of shifted Legendre polynomials. Illustrative examples are included to demonstrate the validity and applicability of the presented technique and a comparison is made with existing results.