Numerical Strategies of the Lorenz's Nonlinear Problems Using Adomian Decomposition Method

Abstract

In this paper an interesting and famous realistic Lorenz's nonlinear problem is discussed using the Adomian Decomposition Method (ADM). The results (approximate solutions) obtained very accurate using classical Runge-Kutta (RK) method, single-term Haar Wavelet series (8) and ADM methods are compared with the ODE45 in Matlab. It is found that the solution obtained using ADM is closer to the ODE45 in Matlab. The high accuracy and the wide applicability of ADM approach will be demonstrated with numerical example. Solution graphs for discrete exact solutions are presented in a graphical form to show the efficiency of the ADM. The results obtained show that ADM is more useful for solving Lorenz's nonlinear problems and the solution can be obtained for any length of time.