Numerov's method for non-linear two-point boundary value problems

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.

Keywords:

• Finite difference equations
• two-point boundary value problem
• non-linear
• numerov's method
• convergence

C.R. Categories:

• G.1.7