Numerical aspect of Predator-Pray Model

In a closed eco-system, there are only two types of animals: the predator and the prey. They form a simple food-chain where the predator species hunts the prey species, while the prey grazes vegetation. The size of the two populations can be described by a simple system of two nonlinear first order differential equations formally known as the Lotka-Volterra equations, which originated in the study of fish populations of the Mediterranean during and immediately after World War I. Here, we study numerically this nonlinear parabolic evolution problem and compare the result of various numerical schemes.