On Numerov's method for a class of strongly nonlinear two-point boundary value problems

Authors:
Yuan-Ming Wang
Affiliations:
Department of Mathematics, East China Normal University, Shanghai 200241, People's Republic of China and Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Sci ...
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

The purpose of this paper is to give a numerical treatment for a class of strongly nonlinear two-point boundary value problems. The problems are discretized by fourth-order Numerov's method, and a linear monotone iterative algorithm is presented to compute the solutions of the resulting discrete problems. All processes avoid constructing explicitly an inverse function as is often needed in the known treatments. Consequently, the full potential of Numerov's method for strongly nonlinear two-point boundary value problems is realized. Some applications and numerical results are given to demonstrate the high efficiency of the approach.