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

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.

This paper can be downloaded at: http://www.depts.ttu.edu/coe/CARES/pdf/Wang_Atluri_2016.pdf

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