Direct-Search Methods for the Solution of the Two-Point Boundary Value Problem (TPBVP)
Technical document Jul 1968-Jul 1969
NAVAL ELECTRONICS LAB CENTER SAN DIEGO CA
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Direct-search algorithms developed in the study of mathematical programming are applied to the solution of a TPBVP. The TPBVP is formulated as an unconstrained minimization problem the solution of which depends on the unknown initial conditions of the differential equations. Search schemes perturb these variables and minimize an objective function. This approach requires integration of the differential equations for each evaluation of the objective function. Three search methods are tried on an Earth-Mars trajectory - the method of Hooke and Jeeves, the method of Flood and Leon, and an improved version of Powells method. Some typical results are tabulated. The methods are simple to formulate and implement. Computer storage requirements and convergence sensitivity are minimal. Convergence time is a function of search step size delta, which determines how the parameters are changed, and search acceleration factor rho. The method used to numerically integrate the differential equations also has a direct effect upon convergence time.
- Numerical Mathematics