Thermal Science

International Scientific Journal

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Jun-Feng Lu

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

generalized differential transform method, Padé approximation, Belov-Chaltikian lattice

PAPER SUBMITTED: 2013-01-18

PAPER REVISED: 2013-04-26

PAPER ACCEPTED: 2013-05-01

PUBLISHED ONLINE: 2013-12-28

DOI REFERENCE: https://doi.org/10.2298/TSCI1305305L

CITATION EXPORT: view in browser or download as text file

THERMAL SCIENCE YEAR 2013, VOLUME 17, ISSUE No. 5, PAGES [1305 - 1310]

REFERENCES

[1] Wu, G. C., et al., Differential-Difference Model for Textile Engineering, Chaos Soliton. Fract., 42 (2009), 1, pp. 352-354, 10.1016/j.chaos.2008.12.011

[2] Zhi, Q., Qiang, Z., Differential-Difference Regularization for a 2D Inverse Heat Conduction Problem, Inverse Probl., 26 (2010), 9, pp. 95015-95030, 10.1088/0266-5611/26/9/095015

[3] He, J.-H., Nanoscale Flow: Reliable, Efficient and Promising, Thermal Science, 16 (2012), 5, pp. VIIVIII

[4] He, J.-H., Asymptotic Methods for Solitary Solutions and Compactons, Abstr. Appl. Anal., Vol. 2012, Article ID 916793, 10.1155/2012/916793

[5] Fermi, E., et al., The Collected Papers of Enrico Fermi, Chicago Press, Chicago, Ill, USA, 1965, 10.1016/0368-3230(66)90138-8

[6] 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, 10.1016/j.cpc.2004.07.002

[7] 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, 10.1063/1.532230

[8] 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

[9] 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, 10.1063/1.1378306

[10] 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, 10.1088/0256-307x/29/10/100201

[11] Adomian, G., A Review of the Decomposition Method in Applied Mathematics, J. Math. Anal. Appl., 135 (1988), 2, pp. 501-544, 10.1016/0022-247x(88)90170-9

[12] He, J.-H., Wu, X.-H., Exp-Function Method for Non-linear Wave Equations, Chaos Soliton. Fract., 30 (2006), 3, pp. 700-708, 10.1016/j.chaos.2006.03.020

[13] 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, 10.1016/j.physleta.2007.07.051

[14] Yang P., et al., ADM-Padé Technique for the Non-linear Lattice Equations, Appl. Math. Comput., 210 (2009), pp. 362-375

[15] Pukhov, G. E., Differential Transformations and Mathematical Modeling of Physical Processes, Naukova Dumka, Kiev, Ukraine, 1986

[16] Baker, G. A., Essential of Padé Approximants, Academic Press, London, UK, 1975

[17] Li, Z., et al., Generalized Differential Transform Method to Differential-Difference Equation, Phys. Lett. A, 373 (2009), 45, pp. 4142-4151, 10.1016/j.physleta.2009.09.036

[18] 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, 10.1016/s0096-3003(98)10115-7

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GDTM-Padé technique for the non-linear differential-difference equation

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence