Higher Order Sensitivities for Solving Nonlinear Two-Point Boundary-Value Problems

In this paper, we consider new computational approaches for solving nonlinear TwoPoint Boundary-Value Problems. The sensitivity calculations required in the solution utilize the automatic differentiation tool OCEA (Object Oriented Coordinate Embedding Method). OCEA has broad potential in this area and many other areas since the partial derivative calculations required for solving these problems are automatically computed and evaluated freeing the analyst from deriving and coding them. In this paper, we demonstrate solving nonlinear Two-Point Boundary Value Problems by shooting and direct methods using automatic differentiation. We demonstrate standard first-order algorithms and higherorder extensions. Additionally, automatic generation of co-state differential equations and secondand higher-order midcourse corrections are considered. Optimization of a sample Low-thrust, Mars-Earth trajectory is considered as an example. Computational issues related to domain of convergence and rate of convergence will be detailed.