Application Of Adomian Decomposition Method In N-S Equation And Landau-Lifshitz Equation

In recent years, Fractional Differential Equation has being more and more widelyused in the description of physical, chemical, biological and medical problems. Thereis an increasing number of foreign scholars pay attention to Fractional DifferentialTheory. Although Fractional Differential Equation can be used to describe realisticproblem elegantly, it leads to great difficulties in analysis and calculation because ofits particularity----memory retention.Adomian Decomposition, also known as Inverse Operator Method was putforward by American mathematic physicist George·Adomian. It has goodconvergence and can be conducted easily in calculation. The main principles of theAdomian method are： fristly, thesolved the equations are into linear parts andnonlinear parts and the solutions of the equations are resolved into infinitecomponents; Secondly, the particular pdynomials, which are equivalent to nonlinearparts of the equations, are created; and finally, components are gradually calculatedfrom low order. So We can get approximate solutions, even exact solutions in thecalculation of Fractional Differential Equation by using Adomian DecompositionMethod. Due to the different definition of the initial term, may appear the phenomnonof “noise”. If there is a phenomenon of “noise”, the solutions of equations are exactsolutions.This paper introduces several definitions and have some important propertiesof fractional order calculus proofed. Introduced the Adomian decomposition methodand the principle of the convergenceAccording to the characteristics of Adomian Decomposition Method, this thesissolved the exact solutions of the3D time fractional incompressible N-S equationbased on a certain initial value. It also solved the approximate solutions of L-Lequation under the condition of first initial value.