A Unification of the Concepts of the Variational Iteration, Adomian Decomposition and Picard Iteration Methods;and a Local Variational Iteration Method  

作　　者：Xuechuan Wang Satya N.Atluri 

机构地区：[1]Texas Tech University,Center for Advanced Research in the Engineering Sciences [2]Northwestern Polytechnical University,China

出　　处：《Computer Modeling in Engineering & Sciences》2016年第6期567-585,共19页工程与科学中的计算机建模（英文）

摘　　要：This paper compares the variational iteration method(VIM),the Adomian decomposition method(ADM)and the Picard iteration method(PIM)for solving a system of first o rder n onlinear o rdinary d ifferential e quations(ODEs).A unification of the concepts underlying these three methods is attempted by considering a very general iterative algorithm for VIM.It is found that all the three methods can be regarded as special cases of using a very general matrix of Lagrange multipliers in the iterative algorithm of VIM.The global variational iteration method is briefly reviewed,and further recast into a Local VIM,which is much more convenient and capable of predicting long term complex dynamic responses of nonlinear systems even if they are chaotic.

关 键 词：VARIATIONAL ITERATION METHOD Adomian decomposition METHOD PICARD ITERATION METHOD ASYMPTOTIC technique nonlinear DYNAMICAL system 

分 类 号：O17[理学—数学]