Existence and Numerical Method for Nonlinear Third-Order Boundary Value Problem in the Reproducing Kernel Space

Xueqin Lü; Minggen Cui

doi:10.1155/2010/459754

Research Article

Open Access

Existence and Numerical Method for Nonlinear Third-Order Boundary Value Problem in the Reproducing Kernel Space

Xueqin Lü^{1, 2}Email author and
Minggen Cui¹

Boundary Value Problems20102010:459754

https://doi.org/10.1155/2010/459754

Received: 14 July 2009

Accepted: 11 January 2010

Published: 2 February 2010

Abstract

We are concerned with general third-order nonlinear boundary value problems. An existence theorem of solution is given under weaker conditions. In the meantime, an iterative algorithm with global convergence is presented. The higher order derivatives of approximate solution is obtained by using this method can approximate the corresponding derivatives of exact solution well.

Keywords

Differential EquationExact SolutionPartial Differential EquationOrdinary Differential EquationApproximate Solution

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Authors’ Affiliations

(1)

Department of Mathematics, Harbin Institute of Technology, Weihai, China

(2)

School of Mathematics and Sciences, Harbin Normal University, Harbin, China

Copyright

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.