Boundary Value Problems
Volume 2008 (2008), Article ID 963753, 22 pages
doi:10.1155/2008/963753

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 t=t0, t=ξ, and t=t1 in a general setting, where t0<ξ<t1. 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 r∈(0,1). The best r 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.