关键词: 两点边值问题, 打靶方法

Abstract: This paper deals with the numerical solutions for nonlinear boundary value problems governed by ordinary differential equations. The nonlinear functions are locally linearized sequentially and a shooting method is then applied to the linearilized equations.This technique is found to be faster in numerical convergence compared with a standard shooting method (i. e. when it is applied directly to the original nonlinear equations). A further reduction in computer time expenditure can be made with the utilization of interpolation to the Jacobian matrices. The present method is simple and easy to be programmed. By making use an exchange process technique of the internal storage requirements with the external equipments of a machine, one may analysis, with the present method, a rather large and complicated problem in a personal computer. A numerical example shows that the present method requires much fewer iterative steps to reach convergence than some finite difference scheme combined with Newton's method does.

Key words: Two-point boundary value problem, shooting method