THERMAL SCIENCE
International Scientific Journal
GDTM-PADé TECHNIQUE FOR THE NON-LINEAR DIFFERENTIAL-DIFFERENCE EQUATION
ABSTRACT
This paper focuses on applying the GDTM-Padé technique to solve the non-linear differential-difference equation. The bell-shaped solitary wave solution of Belov-Chaltikian lattice equation is considered. Comparison between the approximate solutions and the exact ones shows that this technique is an efficient and attractive method for solving the differential-difference equations.
KEYWORDS
PAPER SUBMITTED: 2013-01-18
PAPER REVISED: 2013-04-26
PAPER ACCEPTED: 2013-05-01
PUBLISHED ONLINE: 2013-12-28
THERMAL SCIENCE YEAR
2013, VOLUME
17, ISSUE
Issue 5, PAGES [1305 - 1310]
- Wu, G. C., et al., Differential-Difference Model for Textile Engineering, Chaos Soliton. Fract., 42 (2009), 1, pp. 352-354
- Zhi, Q., Qiang, Z., Differential-Difference Regularization for a 2D Inverse Heat Conduction Problem, Inverse Probl., 26 (2010), 9, pp. 95015-95030
- He, J.-H., Nanoscale Flow: Reliable, Efficient and Promising, Thermal Science, 16 (2012), 5, pp. VIIVIII
- He, J.-H., Asymptotic Methods for Solitary Solutions and Compactons, Abstr. Appl. Anal., Vol. 2012, Article ID 916793
- Fermi, E., et al., The Collected Papers of Enrico Fermi, Chicago Press, Chicago, Ill, USA, 1965
- Baldwin, D., et al., Symbolic Computation of Hyperbolic Tangent Solutions for Non-linear Differential- Difference Equations, Comput. Phys. Commun., 162 (2004), 3, pp. 203-217
- Levi, D., Yamilov, R. I., Conditions for the Existence of Higher Symmetries of Evolutionary Equations on a Lattice, J. Math. Phys., 38 (1997), 12, pp. 6648-6674
- Belov, A. A., Chaltikian, K. D., Lattice Analogues of W-Algebras and Classical Integrable Equations, Phys. Lett. B, 309 (1993), 3-4, pp. 268-274
- Sahadevan, R., Khousalya, S., Similarity Reduction, Generalized Symmetries and Integrability of Belov- Chaltikian and Blaszak-Marciniak Lattice Equation, J. Math. Phys. 42 (2001), 8, pp. 3854-3870
- Xue, B., Wang, X., The Darboux Transformation and New Explicit Solutions for the Belov-Chaltikian Lattice, Chin. Phys. Lett. 29 (2012), 10, pp. 100201-100204
- Adomian, G., A Review of the Decomposition Method in Applied Mathematics, J. Math. Anal. Appl., 135 (1988), 2, pp. 501-544
- He, J.-H., Wu, X.-H., Exp-Function Method for Non-linear Wave Equations, Chaos Soliton. Fract., 30 (2006), 3, pp. 700-708
- Wang, M.-L., et al., The G'/G Expansion Method and Travelling Wave Solutions of Non-linear Evolution Equations in Mathematical Physics, Phys. Lett. A, 372 (2008), 4, pp. 417-423
- Yang P., et al., ADM-Padé Technique for the Non-linear Lattice Equations, Appl. Math. Comput., 210 (2009), pp. 362-375
- Pukhov, G. E., Differential Transformations and Mathematical Modeling of Physical Processes, Naukova Dumka, Kiev, Ukraine, 1986
- Baker, G. A., Essential of Padé Approximants, Academic Press, London, UK, 1975
- Li, Z., et al., Generalized Differential Transform Method to Differential-Difference Equation, Phys. Lett. A, 373 (2009), 45, pp. 4142-4151
- Chen, C.-K., Ho, S.-H., Solving Partial Differential Equations by Two-Dimensional Differential Transform Method, Appl. Math. Comput., 106 (1999), 2-3, pp. 171-179