Adomian Decomposition Method For Solving A Class Of First Order Nonlinear Coupled System

In this paper we study coupled systems of two nonlinear differential equations for first-order, it can be solved with some techniques and Adomian decomposition method,in particular , Adomian decomposition method is efficient mathematic method which can efficiently solve linear or nonlinear equations of math and physical, coupled systems of two nonlinear differential equations for first-order is the most important coupled system ,so many people worked hard at it.In the paper, a class of coupled system of two nonlinear equation for first-order is disussed, which is from model of competition, the coupled system include the original coupled system proposed by Lazhar Bougoffa and Smail Bougouffa ,moreover, it also discuss arithmetic of calculating Adomain's polynomials , Adomain's polynomials play a key role in Adomian decomposition method.At last, this paper present condition which is satisfied by coupled system ,at the same time the coupled system can be decoupled by Adomian decomposition method, the result expand the existed ending, a few simple examples are also studied to show how the Adomian decomposition method works efficiently.