The numerical solution of unstable two point boundary value problems

摘要

A number of workers have tried to solve, numerically, unstable two point boundary value problems. Multiple Shooting and Continuation Methods have been used very successfully for these problems, but each has weaknesses; for particularly unstable problems their success may be partial. In this paper we develop an algorithm that attempts to solve these problems in a routine manner.The algorithm uses a combination of Multiple Shooting and Range Extension in such a way that the advantages of both are maintained while the effects of their disadvantages are reduced considerably. The success of the algorithm is demonstrated on some particularly unstable problems.