TY  - EJOU
AU  - Wang, Xuechuan  
AU  - Atluri, Satya N.  

TI  - A Unification of the Concepts of the Variational Iteration, Adomian Decomposition and Picard Iteration Methods; and a Local Variational Iteration Method
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2016
VL  - 111
IS  - 6
SN  - 1526-1506

AB  - 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 order nonlinear ordinary differential equations (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.
KW  - Variational iteration method
KW  -  Adomian decomposition method
KW  -  Picard iteration method
KW  -  asymptotic technique
KW  -  nonlinear dynamical system

DO  - 10.3970/cmes.2016.111.567