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A Two-Stage LGSM for Three-Point BVPs of Second-Order ODEs

Abstract

The study in this paper is a numerical integration of second-order three-point boundary value problems under two imposed nonlocal boundary conditions at , , and in a general setting, where . We construct a two-stage Lie-group shooting method for finding unknown initial conditions, which are obtained through an iterative solution of derived algebraic equations in terms of a weighting factor . The best is selected by matching the target with a minimal discrepancy. Numerical examples are examined to confirm that the new approach has high efficiency and accuracy with a fast speed of convergence. Even for multiple solutions, the present method is also effective to find them.

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Correspondence to Chein-Shan Liu.

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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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Liu, CS. A Two-Stage LGSM for Three-Point BVPs of Second-Order ODEs. Bound Value Probl 2008, 963753 (2008). https://doi.org/10.1155/2008/963753

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
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