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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 105414, 6 pages
A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations
1Department of Basic Sciences and Humanities, EME College, National University of Sciences and Technology (NUST), Peshawar Road, Rawalpindi 46000, Pakistan
2Department of Mathematics, Statistics and Physics, Qatar University, P.O. Box 2713, Doha, Qatar
3School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad 44000, Pakistan
Received 24 April 2014; Revised 7 July 2014; Accepted 8 July 2014; Published 22 July 2014
Academic Editor: Bashir Ahmad
Copyright © 2014 Mazhar Iqbal 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.
- W. F. Ames, Nonlinear Partial Differential Equations in Engineering, vol. I, Academic Press, New York, NY, USA, 1965.
- H. Azad, M. T. Mustafa, and M. Ziad, “Group classification, optimal system and optimal reductions of a class of Klein Gordon equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 5, pp. 1132–1147, 2010.
- A. H. Bokhari, M. T. Mustafa, and F. D. Zaman, “An exact solution of a quasilinear Fisher equation in cylindrical coordinates,” Nonlinear Analysis, vol. 69, no. 12, pp. 4803–4805, 2008.
- M. T. Mustafa and K. Masood, “Symmetry solutions of a nonlinear elastic wave equation with third-order anharmonic corrections,” Applied Mathematics and Mechanics, vol. 30, no. 8, pp. 1017–1026, 2009.
- G. W. Bluman and J. D. Cole, Similarity Methods for Differential Equations, Springer, New York, NY, USA, 1974.
- G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer, New York, NY, USA, 1989.
- A. G. Hansen, Similarity Analyses of Boundary Value Problems in Engineering, Prentice Hall, Englewood Cliffs, NJ, USA, 1964.
- P. E. Hydon, Symmetry Methods for Differential Equations, Cambridge University Press, Cambridge, UK, 2000.
- N. H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, John Wiley & Sons, Chichester, UK, 1999.
- W. Miller, Symmetry and Separation of Variables, Addison-Wesley, Reading, Mass, USA, 1977.
- P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, NY, USA, 1986.
- L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, NY, USA, 1982.
- H. Azad, M. T. Mustafa, and A. F. M. Arif, “Analytic solutions of initial-boundary-value problems of transient conduction using symmetries,” Applied Mathematics and Computation, vol. 215, no. 12, pp. 4132–4140, 2010.
- G. W. Bluman, “Applications of the general similarity solution of the heat equation to boundary-value problems,” Quarterly of Applied Mathematics, vol. 31, pp. 403–415, 1974.
- B. J. Cantwell, Introduction to Symmetry Analysis, Cambridge University Press, Cambridge, UK, 2002.
- R. P. Agarwal and D. O'Regan, “Infinite interval problems modeling the flow of a gas through a semi-infinite porous medium,” Studies in Applied Mathematics, vol. 108, no. 3, pp. 245–257, 2002.
- R. P. Agarwal and D. O'Regan, “Non-linear boundary value problems on the semi-infinite interval: an upper and lower solution approach,” Mathematika, vol. 49, no. 1-2, pp. 129–140, 2002.
- R. E. Kidder, “Unsteady flow of gas through a semi-infinite porous medium,” Journal of Applied Mechanics, vol. 27, pp. 329–332, 1957.
- T. Y. Na, Computational Methods in Engineering Boundary Value Problems, vol. 145 of Mathematics in Science and Engineering, Academic Press, New York, NY. USA, 1979.
- M. Muskat, Flow of Homogeneous Fluids, J. Edwards, Ann Arbor, Mich, USA, 1946.
- Y. Khan, N. Faraz, and A. Yildirim, “Series solution for unsteady gas equation via Mldm—Pade Technique,” World Applied Sciences Journal, vol. 10, pp. 1452–1456, 2010.
- M. A. Noor and S. T. Mohyud-Din, “Variational iteration method for unsteady flow of gas through a porous medium using He's polynomials and Pade approximants,” Computers & Mathematics with Applications, vol. 58, no. 11-12, pp. 2182–2189, 2009.
- A. Wazwaz, “The modified decomposition method applied to unsteady flow of gas through a porous medium,” Applied Mathematics and Computation, vol. 118, no. 2-3, pp. 123–132, 2001.
- S. C. Anco and G. Bluman, “Direct constructi on method for conservation laws of partial di ff erential equations part I: examples of c onservation law classifications,” European Journal of Applied Mathematics, vol. 13, no. 5, pp. 545–566, 2002.
- S. C. Anco and G. Bluman, “Direct construction method for conservation laws of partial differential equations part II: general treatment,” European Journal of Applied Mathematics, vol. 13, no. 5, pp. 567–585, 2002.
- T. Wolf, “A comparison of four approaches to the calculation of conservation laws,” European Journal of Applied Mathematics, vol. 13, no. 2, pp. 129–152, 2002.
- L. Dresner, Similarity Solutions of Nonl inear Partial Differential Equations, vol. 88 of Research Notes in Mathematics Series, Longman, 1983.
- M. M. Rashidi, T. Hayat, E. Erfani, S. A. M. Pour, and A. A. Hendi, “Simultaneous effects of partial slip and thermal-diffusion and diffusion-thermo on steady MHD convective flow due to a rotating disk,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 11, pp. 4303–4317, 2011.
- M. M. Rashidi, S. A. Mohimanian Pour, T. Hayat, and S. Obaidat, “Analytic approximate solutions for steady flow over a rotating disk in porous medium with heat transfer by homotopy analysis method,” Computers & Fluids, vol. 54, no. 1, pp. 1–9, 2012.