A modified simple shooting method for solving two-point boundary value problems

In physics and engineering, one often encounters what is called a two-point boundary value problem (TPBVP). Several methods exist, for solving these problems. Shooting methods, such as the Simple Shooting Method (SSM) and its variation, the Multiple Shooting Method (MSM) are two popular methods used to solve TPBVPs.

In this thesis, a new method is proposed that was designed from the favorable aspects of both the simple and the multiple shooting methods. 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 Modified Simple Shooting Method is proven under mild conditions on the TPBVP. A comparison of the multiple and the modified simple shooting methods is made for some cases where both methods converge. Finally, we study a TPBVP arising from Pontryagin's Maximum principle applied to an six-degree-of-freedom aircraft model, for which the MSSM converges while the MSM fails to converge.