Comparison of Legendre polynomial approximation and variational iteration method for the solutions of general linear Fredholm integro-differential equations

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dc.contributor.authorBildik N.
dc.contributor.authorKonuralp A.
dc.contributor.authorYalçinbaş S.
dc.date.accessioned2024-07-22T08:21:02Z
dc.date.available2024-07-22T08:21:02Z
dc.date.issued2010
dc.description.abstractIn this study it is shown 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. © 2009 Elsevier Ltd. All rights reserved.
dc.identifier.DOI-ID10.1016/j.camwa.2009.06.022
dc.identifier.issn08981221
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/18433
dc.language.isoEnglish
dc.rightsAll Open Access; Hybrid Gold Open Access
dc.subjectIntegrodifferential equations
dc.subjectIterative methods
dc.subjectNumerical methods
dc.subjectExact solution
dc.subjectFredholm
dc.subjectInitial approximation
dc.subjectInitial functions
dc.subjectLegendre polynomials
dc.subjectNumerical solution
dc.subjectVariational iteration method
dc.subjectPolynomial approximation
dc.titleComparison of Legendre polynomial approximation and variational iteration method for the solutions of general linear Fredholm integro-differential equations
dc.typeArticle

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