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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 146976, 7 pages
Invariant Solutions for Nonhomogeneous Discrete Diffusion Equation
1Department of Mathematics, University of Azad Jammu & Kashmir, Muzaffarabad 13100, Pakistan
2Department of Mathematics, COMSATS Institute, Abbottabad 22010, Pakistan
Received 29 April 2013; Accepted 18 August 2013
Academic Editor: R. Sahadevan
Copyright © 2013 M. N. Qureshi 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.
- S. Goldberg, Introduction to Difference Equations, with Illustrative Examples from Economics, Psychology, and Sociology, John Wiley & Sons, New York, NY, USA, 1958.
- C. Jordan, Calculus of Finite Differences, Chelsea Publishing CompanyBronx, New York, NY, USA, 3rd edition, 1965.
- R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York, NY, USA, 1963.
- P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, NY ,USA, 1986.
- G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer, New York, NY, USA, 1989.
- D. Levi, L. Vinet, and P. Winternitz, “Lie group formalism for difference equations,” Journal of Physics A, vol. 30, no. 2, pp. 633–649, 1997.
- S. Maeda, “The similarity method for difference equations,” IMA Journal of Applied Mathematics, vol. 38, no. 2, pp. 129–134, 1987.
- G. R. W. Quispel and R. Sahadevan, “Lie symmetries and the integration of difference equations,” Physics Letters A, vol. 184, no. 1, pp. 64–70, 1993.
- Z. Jiang, “Lie symmetries and their local determinacy for a class of differential-difference equations,” Physics Letters A, vol. 240, no. 3, pp. 137–143, 1998.
- J. Campbell, “The SMM Model as a boundary value problem using the discrete heat equation,” NASA Langley Research Center Hampton Virginia, vol. 72, no. 4, pp. 539–546, 2007.
- R. Hernández Heredero, D. Levi, and P. Winternitz, “Symmetries of the discrete Burgers equation,” Journal of Physics A, vol. 32, no. 14, pp. 2685–2695, 1999.
- R. Hernandez Heredero, D. Levi, and P. Winternitz, “Point symmetries and generalized symmetries of nonlinear difference equations,” Preprint CRM 2568, CRM, Montréal, Canada, 1998.
- R. Floreanini and L. Vinet, “Lie symmetries of finite-difference equations,” Journal of Mathematical Physics, vol. 36, no. 12, pp. 7024–7042, 1995.
- P. A. Clarkson and F. W. Nijhoff, Eds., Symmetries and Integrability of Difference Equations, vol. 255 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, UK, 1999.
- J. M. Burgers, ‘The Nonlinear Diffusion Equation’ Asymptotic Solutions and Statistical Problems, Reidel, Dordrecht, The Netherlands, 1974.
- D. Levi and P. Winternitz, “Symmetries and conditional symmetries of differential-difference equations,” Journal of Mathematical Physics, vol. 34, no. 8, pp. 3713–3730, 1993.
- D. Levi and P. Winternitz, “Continuous symmetries of discrete equations,” Physics Letters A, vol. 152, no. 7, pp. 335–338, 1991.
- D. David, N. Kamran, D. Levi, and P. Winternitz, “Subalgebras of loop algebras and symmetries of the Kadomtsev-Petviashvili equation,” Physical Review Letters, vol. 55, no. 20, pp. 2111–2113, 1985.
- R. Hirota, “Nonlinear partial difference equations. V. Nonlinear equations reducible to linear equations,” Journal of Physical Society of Japan, vol. 46, no. 1, pp. 312–319, 1979.
- Z. Y. Lu and Y. Takeuchi, “Global asymptotic behavior in single-species discrete diffusion systems,” Journal of Mathematical Biology, vol. 32, no. 1, pp. 67–77, 1993.
- G. Fáth, “Propagation failure of traveling waves in a discrete bistable medium,” Physica D. Nonlinear Phenomena, vol. 116, no. 1-2, pp. 176–190, 1998.