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