Comparing the multistage and Padé techniques for iterative methods in solving nonlinear food chain model

Abstract

In this article, we illustrate the advantages of using multistage technique to improve the solution obtained via iterative methods for series solution of differential equations. This is accomplished by comparing between the Padé and the multistage techniques when used with the Adomian decomposition method and the differential transformation method. The case study is a system of nonlinear differential equations that describes three species food chain model with Beddington DeAngelis functional response. Numerical simulations illustrate that the multistage technique presents good results in the different cases of the solution of the considered system whereas the Padé technique fails when dealing with the case of periodic solution.