Application of Pade' Homotopy Method to Solve Logistic Lotka–Volterra Problem

Abstract

In this research, the problems of Lotka–Volterra and Lotka–Volterra with prey logistic growth models are solved by using homotopy and Pade' homotopy methods. The homotopy method is an analytical approach to solve non linear problems. The solution of homotopy method is common series. The solution of the problem using Pade' homotopy method is obtained by using the result of applying the homotopy method and then transforming the equation into the form of rational function. The results of homotopy and Pade' homotopy methods are compared with some numerical solutions. The result shows that in solving Lotka–Volterra and Lotka–Volterra with prey logistic growth, the Pade' homotopy method is better than homotopy method because the Pade' homotopy method covers a larger area of convergence and produces smaller errors.