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Boundary Value Problems

, 2008:963753

First Online: 14 July 2008Received: 12 May 2008Accepted: 09 July 2008

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 Open image in new window, Open image in new window, and Open image in new window in a general setting, where Open image in new window. 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 Open image in new window. The best Open image in new window 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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Author: Chein-Shan Liu

Source: https://link.springer.com/



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