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Zbl 1162.65420
Yalçinbaş, Salih; Sezer, Mehmet; Sorkun, Hüseyin Hilmi
Legendre polynomial solutions of high-order linear Fredholm integro-differential equations. (English)
[J] Appl. Math. Comput. 210, No. 2, 334-349 (2009). ISSN 0096-3003

Summary: A Legendre collocation matrix method is presented to solve high-order Linear Fredholm integro-differential equations under the mixed conditions in terms of Legendre polynomials. The proposed method converts the equation and conditions to matrix equations, by means of collocation points on the interval [-1,1], which corresponding to systems of linear algebraic equations with Legendre coefficients. Thus, by solving the matrix equation, Legendre coefficients and polynomial approach are obtained. Also examples that illustrate the pertinent features of the method are presented and by using the error analysis, the results are discussed.

MSC 2000:: *65R20 Integral equations (numerical methods)

Keywords: Legendre polynomials and series; Fredholm integro-differential equations; collocation points

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