A new non-standard finite difference method for autonomous differential equations

Abstract

This paper presents a new approach to constructing Non-Standard Finite Difference Method (NSFDM) for the solution of autonomous Ordinary Differential Equations (ODEs). The need for this method came up due to the 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 new nonstandard finite difference method have the property that its solution do not exhibit numerical instabilities.