Derivation and Validation of an Initial-Value Method for Certain Nonlinear Two-Point Boundary-Value Problems.
Much of the theory of invariant imbedding is devoted to the conversion of boundary-value problems into initial-value (Cauchy) problems because of the computational advantages offered by the initial-value formulation. This study describes a technique for transforming a nonlinear two-point boundary-value problem into an initial-value problem and shows, conversely, that the solution of the Cauchy problem does satisfy the original boundary-value problem. The technique given is broad enough to cover many of the equations of radiative transfer, dilute gas dynamics, and optimal control. 17 pp. Refs.