Abstract
For the numerical solution of non-linear two-point boundary value problems: the well-known Numerov's method leads to a non-linear system for the approximate solution. We consider here application of Newton's method for the solution of the resulting non-linear system. In this note we propose an initial approximation for use with Newton's method and obtain sufficient conditions which guarantee convergence of Newton's method with this initial appro-ximation and for all interestingly, this initial approximation makes use only of the boundary data given in the two-point boundary value problem.
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