A Two-Stage LGSM for Three-Point BVPs of Second-Order ODEs. (14th July 2008) - Liu, Chein-Shan
Abstract : The study in this paper is a numerical integration of second-order three-point boundary value problems under two imposed nonlocal boundary conditions att = t 0, t = ξ, andt = t 1 in a general setting, wheret 0 < ξ < t 1 . 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 factorr ∈ ( 0, 1 ) . The bestr 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.