Modified Simple Shooting Method for Solving Two-Point Boundary-Value Problems

摘要

In the study of mechanics and optimal control, one often encounters what is called a two-point boundary-value problem (TPBVP). A couple of methods exist for solving these problems, such as the Simple Shooting Method (SSM) and its variation, the Multiple Shooting Method (MSM). In this paper a new method is proposed that was designed from the favorable aspects of both the SSM and the MSM. The Modified Simple Shooting Method (MSSM) sheds undesirable aspects of both previously mentioned methods to yield a superior, faster method for solving TPBVPs. The convergence of the MSSM is proven under mild conditions on the TPBVP. A comparison of the MSM and the MSSM is made for a problem where both methods converge. We also provide a second example where the MSM fails to converge while the MSSM converges rapidly.