The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel Method

The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel Method

This paper expands the application of reproducing kernel method to a class of third-order boundary value problems with mixed nonlinear boundary conditions. The analytical solution is represented in the form of series in the reproducing kernel space. The n-term approximation is obtained and is proved...

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Main Authors: Zhiyuan Li, Yulan Wang, Fugui Tan
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/195310
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spelling doaj-00354d4ceb04417aabe6054563f688c02020-11-24T23:38:01ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/195310195310The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel MethodZhiyuan Li0Yulan Wang1Fugui Tan2Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, ChinaDepartment of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, ChinaJining Teachers College, Jining 012000, ChinaThis paper expands the application of reproducing kernel method to a class of third-order boundary value problems with mixed nonlinear boundary conditions. The analytical solution is represented in the form of series in the reproducing kernel space. The n-term approximation is obtained and is proved to converge to the analytical solution. The numerical examples are given to demonstrate the computation efficiency of the presented method. Results obtained by the method indicate that the method is simple and effective.http://dx.doi.org/10.1155/2012/195310
collection DOAJ
language English
format Article
sources DOAJ
author Zhiyuan Li
Yulan Wang
Fugui Tan
spellingShingle Zhiyuan Li
Yulan Wang
Fugui Tan
The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel Method
Abstract and Applied Analysis
author_facet Zhiyuan Li
Yulan Wang
Fugui Tan
author_sort Zhiyuan Li
title The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel Method
title_short The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel Method
title_full The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel Method
title_fullStr The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel Method
title_full_unstemmed The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel Method
title_sort solution of a class of third-order boundary value problems by the reproducing kernel method
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description This paper expands the application of reproducing kernel method to a class of third-order boundary value problems with mixed nonlinear boundary conditions. The analytical solution is represented in the form of series in the reproducing kernel space. The n-term approximation is obtained and is proved to converge to the analytical solution. The numerical examples are given to demonstrate the computation efficiency of the presented method. Results obtained by the method indicate that the method is simple and effective.
url http://dx.doi.org/10.1155/2012/195310
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AT yulanwang thesolutionofaclassofthirdorderboundaryvalueproblemsbythereproducingkernelmethod
AT fuguitan thesolutionofaclassofthirdorderboundaryvalueproblemsbythereproducingkernelmethod
AT zhiyuanli solutionofaclassofthirdorderboundaryvalueproblemsbythereproducingkernelmethod
AT yulanwang solutionofaclassofthirdorderboundaryvalueproblemsbythereproducingkernelmethod
AT fuguitan solutionofaclassofthirdorderboundaryvalueproblemsbythereproducingkernelmethod
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