2016 International Symposium on Nanofluid Heat and Mass Transfer in Textile Engineering and 5th International Symposium on Nonlinear Dynamics


Journal: Nonlinear Science Letters A
(ISSN 2519-9072(Online), ISSN 2076-2275 (Print))          Vol. 1 No. 2
A Modified Variational Iteration Method for Strongly Nonlinear Problems
Nicolae Herişanu1,2, Vasile Marinca1,2
1. Politehnica University of Timişoara, Bd.Mihai Viteazu, nr.1, 300222 Timişoara, Romania
2. Center for Advanced and Fundamental Technical Research, Romanian Academy, Timisoara Branch, Bd. M.Viteazu, nr.24, 300223 Timişoara, Romania
Abstract: A modified variational iteration method is proposed combining the features of the classical VIM with a rigorous computational algorithm for minimizing the residual functional, which provides a simple procedure to control the convergence of the results. This optimization procedure, namely the Optimal Variational Iteration Method (OVIM) is used for analytically solving the Duffing-harmonic oscillator. This method provides a good approximation for both angular frequency and approximate periodic solution. The proposed procedure yields rapid convergence to the exact solution. Its effectiveness is illustrated by some examples and a very good agreement is found between the results obtained through the proposed procedure and numerical simulation results.

Keywords: Optimal Variational Iteration Method (OVIM), Duffing-harmonic oscillator

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