Abstract
A theoretical foundation is established for the numerical phase of a symbolic-numeric method for solving nonlinear, two-point, boundary value problems. The method, applicable to holomorphic systems, involves the formal (symbolic) solution of the differential system by means of two-point series. This is followed by an iterative numerical phase that produces a series satisfying the boundary value problem. Conditions are established under which the numerical phase is well defined and converges. The former problem involves the existence and local uniqueness of solutions to a constrained version of the boundary conditions and to certain initial value problems. A subsequent article will study the method as a practical computational algorithm.
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