Effective Boundary Value Problem Solver via Bézier Functions

Abstract

In engineering disciplines, many important problems are to be formed as boundary value problems (BVPs) that have conditions that are specified at the extremes. To handle such problems, the conventional shooting method that transforms BVPs into initial value problems has been extensively used, but it does not always guarantee solving the problem due to the possible failure of finding a proper initial guess. This paper proposes a universal initial guess finder that is composed of Bézier functions. Various dimensional problems that include Lambert’s problem for several orbits around the spherically symmetric Earth are studied to validate the efficacy of the proposed approach, and the results are compared.

Keywords

• boundary value problem
• Bézier functions
• initial guess finder