A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation

The aim of this paper is to apply OHAM to solve numerically the problem of harmonic wave propagation in a nonlinear thermoelasticity under influence of rotation, thermal relaxation times, and magnetic field. The problem is solved in one-dimensional elastic half-space model subjected initially to a p...

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Main Authors: S. M. Abo-Dahab, Mohamed S. Mohamed, T. A. Nofal
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/614874
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author S. M. Abo-Dahab
Mohamed S. Mohamed
T. A. Nofal
author_facet S. M. Abo-Dahab
Mohamed S. Mohamed
T. A. Nofal
author_sort S. M. Abo-Dahab
collection DOAJ
description The aim of this paper is to apply OHAM to solve numerically the problem of harmonic wave propagation in a nonlinear thermoelasticity under influence of rotation, thermal relaxation times, and magnetic field. The problem is solved in one-dimensional elastic half-space model subjected initially to a prescribed harmonic displacement and the temperature of the medium. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution. This optimal approach has a general meaning and can be used to get fast convergent series solutions of the different type of nonlinear fractional differential equation. The displacement and temperature are calculated for the models with the variations of the magnetic field, relaxation times, and rotation. The results obtained are displayed graphically to show the influences of the new parameters.
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institution Kabale University
issn 1085-3375
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publishDate 2013-01-01
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series Abstract and Applied Analysis
spelling doaj-art-b003f656bdc5483587f2996fd7827c0b2025-08-20T03:39:17ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/614874614874A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of RotationS. M. Abo-Dahab0Mohamed S. Mohamed1T. A. Nofal2Mathematics Department, Faculty of Science, Taif University, P.O. Box 888, Saudi ArabiaMathematics Department, Faculty of Science, Taif University, P.O. Box 888, Saudi ArabiaMathematics Department, Faculty of Science, Taif University, P.O. Box 888, Saudi ArabiaThe aim of this paper is to apply OHAM to solve numerically the problem of harmonic wave propagation in a nonlinear thermoelasticity under influence of rotation, thermal relaxation times, and magnetic field. The problem is solved in one-dimensional elastic half-space model subjected initially to a prescribed harmonic displacement and the temperature of the medium. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution. This optimal approach has a general meaning and can be used to get fast convergent series solutions of the different type of nonlinear fractional differential equation. The displacement and temperature are calculated for the models with the variations of the magnetic field, relaxation times, and rotation. The results obtained are displayed graphically to show the influences of the new parameters.http://dx.doi.org/10.1155/2013/614874
spellingShingle S. M. Abo-Dahab
Mohamed S. Mohamed
T. A. Nofal
A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation
Abstract and Applied Analysis
title A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation
title_full A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation
title_fullStr A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation
title_full_unstemmed A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation
title_short A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation
title_sort one step optimal homotopy analysis method for propagation of harmonic waves in nonlinear generalized magnetothermoelasticity with two relaxation times under influence of rotation
url http://dx.doi.org/10.1155/2013/614874
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