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

Dates

  • Submission Date2013-01-18
  • Revision Date2013-04-26
  • Acceptance Date2013-05-01
  • Online Date2013-12-28

DOI Reference

10.2298/TSCI1305305L

References

  1. Wu, G. C., et al., Differential-Difference Model for Textile Engineering, Chaos Soliton. Fract., 42 (2009), 1, pp. 352-354
  2. Zhi, Q., Qiang, Z., Differential-Difference Regularization for a 2D Inverse Heat Conduction Problem, Inverse Probl., 26 (2010), 9, pp. 95015-95030
  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
  5. Fermi, E., et al., The Collected Papers of Enrico Fermi, Chicago Press, Chicago, Ill, USA, 1965
  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
  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
  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. 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
  11. Adomian, G., A Review of the Decomposition Method in Applied Mathematics, J. Math. Anal. Appl., 135 (1988), 2, pp. 501-544
  12. He, J.-H., Wu, X.-H., Exp-Function Method for Non-linear Wave Equations, Chaos Soliton. Fract., 30 (2006), 3, pp. 700-708
  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
  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
  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
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