@Article{cmes.2016.111.567,
AUTHOR = {Xuechuan  Wang, Satya N.  Atluri},
TITLE = {A Unification of the Concepts of the Variational Iteration, Adomian Decomposition and Picard Iteration Methods; and a Local Variational Iteration Method},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {111},
YEAR = {2016},
NUMBER = {6},
PAGES = {567--585},
URL = {http://www.techscience.com/CMES/v111n6/27334},
ISSN = {1526-1506},
ABSTRACT = {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.},
DOI = {10.3970/cmes.2016.111.567}
}