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On the solutions of three-point boundary value problems using variational-fixed point iteration method


Citation

Kilicman, Adem and Wadai, Mutah (2016) On the solutions of three-point boundary value problems using variational-fixed point iteration method. Mathematical Sciences, 10 (1). pp. 33-40. ISSN 2008-1359; ESSN: 2251-7456

Abstract

Given a three-point fourth-order boundary value problems y(iv) + p(x)y’’’ + r(x)y’ + s(x)y = f(x), a ≤ x ≤ b such that y(a) = y(b) = y’’(b) = y’’(α) = 0, a ≤ α ≤ b; where p, q, r, s, f ϵ C [a, b] , we combine the application of variational iteration method and fixed point iteration process to construct an iterative scheme called variational-fixed point iteration method that approximates the solution of three-point boundary value problems. The success of the variational or weighted residual method of approximation from a practical point of view depends on the suitable selection of the basis function. The method is self correcting one and leads to fast convergence. Problems were experimented to show the effectiveness and accuracy of the proposed method.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1007/s40096-016-0175-z
Publisher: Springer
Keywords: Fixed point iteration; Variational iteration method; Lagrange's multiplier; Boundary value problems
Depositing User: Nabilah Mustapa
Date Deposited: 03 May 2017 04:28
Last Modified: 03 May 2017 04:28
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1007/s40096-016-0175-z
URI: http://psasir.upm.edu.my/id/eprint/51922
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