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International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Online from: 1991
Subject Area: Mechanical & Materials Engineering
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The use of variational iteration method and homotopy perturbation method for solving two nonlinear equations
| Title: | The use of variational iteration method and homotopy perturbation method for solving two nonlinear equations |
|---|---|
| Author(s): | Manel Labidi, (Ecole Polytechnique de Tunisie, La Marsa, Tunisia), Khaled Omrani, (Institut Superieur des Sciences Appliquées et de Technologie de Sousse, Sousse, Tunisia) |
| Citation: | Manel Labidi, Khaled Omrani, (2011) "The use of variational iteration method and homotopy perturbation method for solving two nonlinear equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 Iss: 4, pp.377 - 398 |
| Keywords: | Differential equations, Iterative methods, Variational techniques |
| Article type: | Research paper |
| DOI: | 10.1108/09615531111123074 (Permanent URL) |
| Publisher: | Emerald Group Publishing Limited |
| Abstract: | Purpose – The purpose of this paper is to implement variational iteration method (VIM) and homotopy perturbation method (HPM) to solve modified Camassa-Holm (mCH) and modified Degasperis-Procesi (mDP) equations. Design/methodology/approach – Perturbation method is a traditional method depending on a small parameter which is difficult to be found for real-life nonlinear problems. To overcome the difficulties and limitations of the above method, two new ones have recently been introduced by He, i.e. VIM and HPM. In this paper, mCH and mDP equations are solved through these methods. Findings – To assess the accuracy of the solutions, the comparison of the obtained results with the exact solutions reveals that both methods are tremendously effective. Originality/value – The paper shows that VIM and HPM can be implemented to solve mCH and mDP equations. |
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