Two-Point Boundary-Value-Problem Techniques

Publisher Summary The theory of ordinary differential equations, subject to initial conditions, is one of the most extensively developed branches of mathematical analysis. Theorems on the existence and uniqueness of solutions are widely available in literature. In turn, the constructive nature of many of the proofs of these theorems has led to successful algorithms for the solution of initial-value problems on electronic computers. For the two-point boundary-value problem, the state of the art, from both analytical and computational points of view, lags behind. The problems of mathematical science that ultimately lead to boundary-value problems are too numerous t o list. In flight mechanics, for example, problems in orbit determination and in intercept and rendezvous studies require the solution of two-point boundary- value. This chapter discusses the boundary-value problem resulting from the application of the Pontryagin maximum principle and inequality constraints on the state space. It also discusses problem formulations and presents a comparison of the Newton–Raphson operator approach with direct methods.

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