IJPAM: Volume 108, No. 4 (2016)

A SEMI ANALYTICAL ITERATIVE TECHNIQUE
FOR SOLVING DUFFING EQUATIONS

M.A. Al-Jawary$^1$, S.G. Al-Razaq$^2$
$^{1,2}$College of Education for Pure Sciences
Ibn-AL-Haithem
Baghdad University
Baghdad, IRAQ


Abstract. This paper presents new implementation of reliable iterative method proposed by Temimi and Ansari namely (TAM) for analytic and numerical solutions of Duffing equations in two types: damping and undamping equations. The solution is obtained in the series form that converge to the exact solution with easily computed components. Several problems are solved to demonstrate the efficiency of the proposed methods without any restrictive assumptions for nonlinear terms. However, for some examples numerical calculations evidenced by tables and figures for the analysis of the maximal error remainder values.The software used for the calculations in this study was MATHEMATICA $ ^\circledR $ 9.0.

Received: May 1, 2016

AMS Subject Classification: 65L05, 34A34, 34A45

Key Words and Phrases: Duffing equation, damping equation, undamping equation, exact solution, iterative method

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DOI: 10.12732/ijpam.v108i4.13 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 4
Pages: 871 - 885


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