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  • Research Article
  • Open Access

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

Boundary Value Problems20102010:459754

  • Received: 14 July 2009
  • Accepted: 11 January 2010
  • Published:


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.


  • Differential Equation
  • Exact Solution
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Approximate Solution

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Authors’ Affiliations

Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong, 264209, China
School of Mathematics and Sciences, Harbin Normal University, Harbin, Heilongjiang, 150025, China


© X. Lü and M. Cui. 2010

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.