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 transforming two-point boundary-value problems into Cauchy problems. Numerous references are given. In this paper, a proof is given that the solution of the Cauchy problem does indeed satisfy the boundary-value problem. The discussion is self-contained and general enough to cover many applications in optimal control and radiative transfer.