Operator splitting methods for the Lotka–Volterra equations

Abstract

Geometric integrators are numerical methods for differential equations that preserve geometric properties. In this article we investigate the questions of constructing such methods for the well-known Lotka–Volterra predator-prey system by using the operator splitting method. We use different numerical methods combined with the operator splitting method and analyse if they preserve the geometric properties of the original system.

Keywords

• numerical methods
• operator splitting
• hamilton systems
• lotka–volterra equations