二階與三階耦合邊值問題的李群 SL(n,R) 打靶法之研究

Abstract

In enginerring and mathematics, boundary value problems are common problems. There are many other form problems that are transformed to boundary value problems. How to accurately solve the boundary value problems is a very important subject for engineers. The coupled boundary value problem is one kind of boundary value problems with two or more equations, and there are interactions between equations. Because of the cross dependencies of equatioms, the difficulty of solving boundary value problems increases. In this study, the numerical solution for two-point boundary value problems is the Lie-group shooting method(LGSM). By using the advandtages of Lie-group`s closure property and quick calculation ,…etc, the one-step group preserving schemes has been used to accurately solve many second-order or third-order boundary value problems. In this paper ,the advantages of using the LGSM for solving the prombles will be extended to two and three-order coupled boundary value prombles. Developing a new form of LGSM, and combining different Lie-groups for solving the coupled boundary value problems. We will prove that the new form LGSM for solving coupled boundary value problem is accurate. After deducing the steps of using LGSM with engineering mathematics and Generalized mid-point rule…etc, we will use one of the commonly used commercial programming language MATLAB to implement steps. We expect LGSM to be extended to more complex boundary value problems, such as high-order coupled, multi-coupled boundary value problems…and so on.