A Two-Stage LGSM for Three-Point BVPs of Second-Order ODEs
© Chein-Shan Liu. 2008
Received: 12 May 2008
Accepted: 9 July 2008
Published: 14 July 2008
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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