The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary Conditions

An iterative algorithm is proposed for solving the solution of a nonlinear fourth-order differential equation with integral boundary conditions. Its approximate solution un(x) is represented in the reproducing kernel space. It is proved that un(x) converges uniformly to the exact solution u(x). More...

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Main Authors: Yanli Fu, Huanmin Yao
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2014/890695
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author Yanli Fu
Huanmin Yao
author_facet Yanli Fu
Huanmin Yao
author_sort Yanli Fu
collection DOAJ
description An iterative algorithm is proposed for solving the solution of a nonlinear fourth-order differential equation with integral boundary conditions. Its approximate solution un(x) is represented in the reproducing kernel space. It is proved that un(x) converges uniformly to the exact solution u(x). Moreover, the derivatives of un(x) are also convergent to the derivatives of u(x). Numerical results show that the method employed in the paper is valid.
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spelling doaj-art-b3add9c098294caf80992928c90caf872025-02-03T06:12:22ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/890695890695The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary ConditionsYanli Fu0Huanmin Yao1School of Mathematics and Sciences, Harbin Normal University, Harbin, Heilongjiang 150025, ChinaSchool of Mathematics and Sciences, Harbin Normal University, Harbin, Heilongjiang 150025, ChinaAn iterative algorithm is proposed for solving the solution of a nonlinear fourth-order differential equation with integral boundary conditions. Its approximate solution un(x) is represented in the reproducing kernel space. It is proved that un(x) converges uniformly to the exact solution u(x). Moreover, the derivatives of un(x) are also convergent to the derivatives of u(x). Numerical results show that the method employed in the paper is valid.http://dx.doi.org/10.1155/2014/890695
spellingShingle Yanli Fu
Huanmin Yao
The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary Conditions
Journal of Function Spaces
title The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary Conditions
title_full The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary Conditions
title_fullStr The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary Conditions
title_full_unstemmed The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary Conditions
title_short The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary Conditions
title_sort solution of nonlinear fourth order differential equation with integral boundary conditions
url http://dx.doi.org/10.1155/2014/890695
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