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

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.

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Correspondence to Xueqin Lü.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Lü, X., Cui, M. Existence and Numerical Method for Nonlinear Third-Order Boundary Value Problem in the Reproducing Kernel Space. Bound Value Probl 2010, 459754 (2010). https://doi.org/10.1155/2010/459754

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Keywords

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