Open Access Research Article

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

Xueqin Lü12* and Minggen Cui1

Author Affiliations

1 Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China

2 School of Mathematics and Sciences, Harbin Normal University, Harbin, Heilongjiang 150025, China

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Boundary Value Problems 2010, 2010:459754  doi:10.1155/2010/459754

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.