Numerical Solutions of Differential Equations System

This book studies a numerical solution of a system of non-linear ordinary differential equations as an application we select a differential system that describes the ecological phenomenon known by the Prey-Predator system also called the Lotka-Volterra model. We illustrate the relation between the performance between the prey and the predator their increasing and decreasing by using a numerical study because we can’t solve this problem analytically. In the practical part we focus on the application of two popular numerical methods: Euler and Range Kutta forth order using numeric computer platform Matlab. The obtained results are a periodic trajectories with two equilibrium points.