A unification of the concepts of the variational iteration, Adomian decomposition and Picard iteration methods; and a local variational iteration method

Xuechuan Wang, Satya N. Atluri

Research output: Contribution to journalArticle

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Abstract

This paper compares the variational iteration method (VIM), the Ado-mian 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 La-grange 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.

Original languageEnglish
Pages (from-to)567-585
Number of pages19
JournalCMES - Computer Modeling in Engineering and Sciences
Volume111
Issue number6
StatePublished - 2016

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