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


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 (, 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).

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