An Explicit Positivity Preserving Scheme: Application to Biological Model

Abstract

This paper deals with the construction of nonstandard finite difference method (NFSD) for nonlinear initial value problems modeled by a system of nonlinear ordinary differential equations. The proposed scheme preserves the positivity property as well as the requirement of conservation law and boundedness. In order to illustrate the accuracy of the new scheme, the numerical results compared with the standard ones.

Keywords: Positivity, Boundedness, Nonstandard finite difference.