Accuracy of the Adomian decomposition method applied to the Lorenz system

A new piecewise-quasilinearization method for solving chaotic systems of initial value problems

“…At these values, the system is known [16] to exhibit chaotic behavior. Because the Lorenz system rapidly oscillates within very small intervals a smaller interval width of ∆ = 0 002 was used to generate accurate results.…”

“…The Lotka-Voltera equations were solved for the general three-species system using the Adomian decomposition method [28] and the multi-stage differential transform method [24]. The Lorenz system was solved using the multi-stage differential transform method [24], the Adomian decomposition method [16] and the multi-stage homotopy analysis method [5]. Approximate analytical or numerical multi-stage methods that have been used to find solutions of the Genesio-Tesi system include, the differential transform method [11], the piecewise-spectral parametric iteration method [13], variational iteration method (VIM) and the multi-stage VIM [14].…”

A new efficient method for solving quadratic Riccati differential equation

“…This methodology was inspired by various researches [35,36,37] who used multistage Adomian decomposition method to solve systems of linear and nonlinear equations. It is a technique which allowed a simple modification of the standard VIM.…”

Efficiency of Differential Transformation Method for Genesio System

“…In recent years, much attention has been devoted to the newly developed methods to construct an analytic solutions of nonlinear equation, such methods include the Adomian decomposition method [2,3,5,6] and the Variational Iteration Method (VIM) [6][7][8] , the homotopy analysis method and the homotopy-perturbation method [9] and homotopy analysis method [9][10][11] . The concept of the Differential Transformation Method (DTM) has been introduced to solve linear and nonlinear initial value problems in electric circuit analysis [1] .…”