Journal of Emerging Trends in Engineering and Applied Sciences: Research Areas

Article Title: On The Theory and Applications of Nonstandard Finite Difference Method for Singular Ordinary Differential Equations
by J. Sunday; E. A. Ibijola and Y. Skwame

Abstract:
This research work presents some basic concepts and applications of a numerical method called the nonstandard finite difference method. Emphasis shall be laid on the construction of nonstandard finite difference method for singular ordinary differential equations. The need for this method came up due to some shortcomings of the standard methods; in which the qualitative properties of the exact solutions are not usually transferred to the numerical solutions. These shortcomings affect the stability of the standard approach. The nonstandard finite difference methods have the property that their solutions do not exhibit numerical instabilities.

Keywords: nonstandard methods, singular ODEs, monotone dependence, difference equations and denominator functions

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