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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 614874, 14 pages
A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation
1Mathematics Department, Faculty of Science, Taif University, P.O. Box 888, Saudi Arabia
2Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
3Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt
4Mathematics Department, Faculty of Science, Minia University, Minia, Egypt
Received 1 May 2013; Revised 2 June 2013; Accepted 4 June 2013
Academic Editor: Santanu Saha Ray
Copyright © 2013 S. M. Abo-Dahab et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- N. H. Sweilam and M. M. Khader, “Variational iteration method for one dimensional nonlinear thermoelasticity,” Chaos, Solitons & Fractals, vol. 32, no. 1, pp. 145–149, 2007.
- N. H. Sweilam, “Harmonic wave generation in non linear thermoelasticity by variational iteration method and Adomian's method,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 64–72, 2007.
- H. N. Sweilam, M. M. Khader, and F. R. Al-Bar, “On the numerical simulation of population dynamics with density-dependent migrations and the Allee effects,” Journal of Physics, vol. 96, no. 1, Article ID 012008, 10 pages, 2008.
- N. H. Sweilam, M. M. Khader, and R. F. Al-Bar, “Nonlinear focusing Manakov systems by variational iteration method and adomian decomposition method,” Journal of Physics, vol. 96, no. 1, Article ID 012164, 7 pages, 2008.
- A. N. Abd-Alla, A. F. Ghaleb, and G. A. Maugin, “Harmonic wave generation in nonlinear thermoelasticity,” International Journal of Engineering Science, vol. 32, no. 7, pp. 1103–1116, 1994.
- C. A. De Moura, “A linear uncoupling numerical scheme for the nonlinear coupled thermo-dynamics equations,” in Numerical Methods, V. Pereyra and A. Reinoze, Eds., vol. 1005 of Lecture Notes in Mathematics, pp. 204–211, Springer, Berlin, Germany, 1983.
- M. Slemrod, “Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity,” Archive for Rational Mechanics and Analysis, vol. 76, no. 2, pp. 97–133, 1981.
- S. J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problem [Ph.D. thesis], Shanghai Jiao Tong University, 1992.
- S. J. Liao, “An approximate solution technique not depending on small parameters: a special example,” International Journal of Non-Linear Mechanics, vol. 30, no. 3, pp. 371–380, 1995.
- K. M. Hemida and M. S. Mohamed, “Numerical simulation of the generalized Huxley equation by homotopy analysis method,” Journal of Applied Functional Analysis, vol. 5, no. 4, pp. 344–350, 2010.
- K. Hemida and M. S. Mohamed, “Application of homotopy analysis method to fractional order generalized Huxley equation,” Journal of Applied Functional Analysis, vol. 7, no. 4, pp. 367–372, 2012.
- M. S. Mohamed, “Analytic approximations for fractional-order Newton-Leipnik system,” Journal of Advanced Research in Scientific Computing, vol. 3, no. 2, pp. 56–69, 2011.
- M. S. Mohamed and H. A. Ghany, “Analytic approximations for fractional-order hyperchaotic system,” Journal of Advanced Research in Dynamical and Control Systems, vol. 3, no. 3, pp. 1–12, 2011.
- H. A. Ghany and M. S. Mohammed, “White noise functional solutions for Wick-type stochastic fractional KdV-Burgers-Kuramoto equations,” Chinese Journal of Physics, vol. 50, no. 4, pp. 619–627, 2012.
- J.-H. He, “Asymptotology by homotopy perturbation method,” Applied Mathematics and Computation, vol. 156, no. 3, pp. 591–596, 2004.
- K. A. Gepreel, S. M. Abo-Dahab, and T. A. Nofal, “Homotopy perturbation method and variational iteration method for harmonic waves propagation in nonlinear magneto-thermoelasticity with rotation,” Mathematical Problems in Engineering, vol. 2012, Article ID 827901, 30 pages, 2012.
- A. M. Abd-Alla and S. M. Abo-Dahab, “Effect of rotation and initial stress on an infinite generalized gagneto-thermoelastic diffusion body with a spherical cavity,” Journal of Thermal Stresses, vol. 35, pp. 892–912, 2012.
- S. M. Abo-Dahab and R. A. Mohamed, “Influence of magnetic field and hydrostatic initial stress on wave reflection from a generalized thermoelastic solid half-space,” JVC/Journal of Vibration and Control, vol. 16, no. 5, pp. 685–699, 2010.
- A. M. Abd-Alla and S. R. Mahmoud, “Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model,” Meccanica, vol. 45, no. 4, pp. 451–462, 2010.
- A. M. Abd-Alla, A. N. Abd-Alla, and N. A. Zeidan, “Thermal stresses in a nonhomogeneous orthotropic elastic multilayered cylinder,” Journal of Thermal Stresses, vol. 23, no. 5, pp. 413–428, 2000.
- A. M. Abd-Alla, S. M. Abo-Dahab, H. A. Hammad, and S. R. Mahmoud, “On generalized magneto-thermoelastic Rayleigh waves in a granular medium under the influence of a gravity field and initial stress,” Journal of Vibration and Control, vol. 17, no. 1, pp. 115–128, 2011.
- A. M. Abd-Alla and S. M. Abo-Dahab, “Time-harmonic sources in a generalized magneto-thermo-viscoelastic continuum with and without energy dissipation,” Applied Mathematical Modelling, vol. 33, no. 5, pp. 2388–2402, 2009.
- M. A. F. Araghia and A. Fallahzadeh, “On the convergence of the Homotopy analysis method for solving the schrodinger equation,” Journal of Applied Sciences Research, vol. 2, pp. 6076–6083, 2012.
- S. Abbasbandy and M. Jalili, “Determination of optimal convergence control parameter value in homotopy analysis method,” Numerical Algorithms, 2013.
- M. Turkyilmazoglu, “Purely analytic solutions of magnetohydrodynamic swirling boundary layer flow over a porous rotating disk,” Computers and Fluids, vol. 39, no. 5, pp. 793–799, 2010.
- M. Turkyilmazoglu, “Numerical and analytical solutions for the flow and heat transfer near the equator of an MHD boundary layer over a porous rotating sphere,” International Journal of Thermal Sciences, vol. 50, no. 5, pp. 831–842, 2011.
- M. Turkyilmazoglu, “Analytic approximate solutions of rotating disk boundary layer flow subject to a uniform suction or injection,” International Journal of Mechanical Sciences, vol. 52, no. 12, pp. 1735–1744, 2010.
- M. Turkyilmazoglu, “Analytic approximate solutions of rotating disk boundary layer flow subject to a uniform vertical magnetic field,” Acta Mechanica, vol. 218, no. 3-4, pp. 237–245, 2011.
- M. Turkyilmazoglu, “A note on the homotopy analysis method,” Applied Mathematics Letters, vol. 23, no. 10, pp. 1226–1230, 2010.