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An important problem that arises in many engineering applications is theboundary value problem for ordinary differential equations. There have beenmany computational methods proposed for dealing with this problem. Theconvergence of the iterative schemes to a true solution, when one such exists,and their numerical stability are the central issues discussed in theliterature. In this paper, we discuss a method for approximating the vectorfield, maintaining the boundary conditions and numerical stability. If a truesolution exists, a subsequence of solutions convergent to one such can beproduced, by finer discretization of the solution space.

Dynamic Programming Method for Best Piecewise Linear Approximation for Vector Field of Nonlinear Boundary Value Problems on the Interval [0, 1]