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


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Article Info

DATE

2016-04-06

AUTHORS

A. Kilicman, M. Wadai

ABSTRACT

Given a three-point fourth-order boundary value problems y(iv)+p(x)y″′+q(x)y″+r(x)y′+s(x)y=f(x),a≤x≤b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} y^{(iv)}+p(x)y^{\prime \prime \prime }+q(x)y^{\prime \prime }+r(x)y^{\prime }+s(x)y=f(x),a \le x \le b \end{aligned}$$\end{document}such that y(a)=y(b)=y″(b)=y″(α)=0,a≤α≤b;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} y(a)=y(b)=y^{\prime \prime }(b)=y^{\prime \prime }(\alpha )=0,a \le \alpha \le b; \end{aligned}$$\end{document}where p,q,r,s,f∈C[a,b]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p,q,r,s,f \in C[a,b]$$\end{document}, 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. More... »

PAGES

33-40

References to SciGraph publications

  • 2013-03-12. The new modified Ishikawa iteration method for the approximate solution of different types of differential equations in FIXED POINT THEORY AND ALGORITHMS FOR SCIENCES AND ENGINEERING
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    http://scigraph.springernature.com/pub.10.1007/s40096-016-0175-z

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