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Zbl 1189.65307
Bildik, Necdet; Konuralp, Ali; Yalç inbaş, Salih
Comparison of Legendre polynomial approximation and variational iteration method for the solutions of general linear Fredholm integro-differential equations. (English)
[J] Comput. Math. Appl. 59, No. 6, 1909-1917 (2010). ISSN 0898-1221

Summary: We show that the numerical solutions of linear Fredholm integro-differential equations obtained by using Legendre polynomials can also be found by using the variational iteration method. Furthermore the numerical solutions of the given problems which are solved by the variational iteration method obviously converge rapidly to exact solutions better than the Legendre polynomial technique. Additionally, although the powerful effect of the applied processes in Legendre polynomial approach arises in the situations where the initial approximation value is unknown, it is shown by the examples that the variational iteration method produces more certain solutions where the first initial function approximation value is estimated. In this paper, the Legendre polynomial approximation (LPA) and the variational iteration method (VIM) are implemented to obtain the solutions of the linear Fredholm integro-differential equations and the numerical solutions with respect to these methods are compared.

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

Keywords: variational iteration method; Legendre polynomial approximation; Fredholm integro-differential equation; integral equation

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Zentralblatt MATH Berlin [Germany]