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Zbl 1193.65229
Saadatmandi, Abbas; Dehghan, Mehdi
Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients. (English)
[J] Comput. Math. Appl. 59, No. 8, 2996-3004 (2010). ISSN 0898-1221

Summary: 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.

MSC 2000:: *65R20 Integral equations (numerical methods)
45J05 Integro-ordinary differential equations

Keywords: differential-difference equation; Fredholm integro-differential-difference equation; tau method; operational matrix; Legendre polynomials; numerical solution

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Zentralblatt MATH Berlin [Germany]