A note on the construction of a 'valid' NSFD scheme for the Lotka-Volterra equations

TL;DR

This paper presents a new explicit NSFD discretization for the Lotka-Volterra equations that maintains all essential properties of the original differential equations, ensuring dynamic consistency.

Contribution

It introduces a novel NSFD scheme that is explicitly constructed to be dynamically consistent with the Lotka-Volterra equations, improving upon previous schemes.

Findings

The scheme preserves the qualitative behavior of the continuous system.

It ensures stability and positivity of solutions.

The method is explicitly constructed for better accuracy.

Abstract

We demonstrate the construction of an explicit NSFD discretization for the standard Lotka-Volterra equations. In contrast to previous NSFD schemes, our representation is dynamic consistent with respect to all the essential properties of the differential equations and their solutions.