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A comparison between two different methods for solving KdV–Burgers equation

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  • Helal, M.A.
  • Mehanna, M.S.

Abstract

This paper presents two methods for finding the soliton solutions to the nonlinear dispersive and dissipative KdV–Burgers equation. The first method is a numerical one, namely the finite differences with variable mesh. The stability of the numerical scheme is discussed. The second method is the semi-analytic Adomian decomposition method. Test example is given. A comparison between the two methods is carried out to illustrate the pertinent feature of the proposed algorithm.

Suggested Citation

  • Helal, M.A. & Mehanna, M.S., 2006. "A comparison between two different methods for solving KdV–Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 320-326.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:2:p:320-326
    DOI: 10.1016/j.chaos.2005.06.005
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    Cited by:

    1. Saka, Bülent, 2009. "Cosine expansion-based differential quadrature method for numerical solution of the KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2181-2190.
    2. Chai, Zhenhua & Shi, Baochang & Zheng, Lin, 2008. "A unified lattice Boltzmann model for some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 874-882.
    3. Abdel-Halim Hassan, I.H., 2008. "Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 53-65.
    4. Ramos, J.I., 2009. "Generalized decomposition methods for nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1078-1084.
    5. Memarbashi, Reza, 2008. "Numerical solution of the Laplace equation in annulus by Adomian decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 138-143.
    6. Gupta, A.K. & Ray, S. Saha, 2018. "On the solution of time-fractional KdV–Burgers equation using Petrov–Galerkin method for propagation of long wave in shallow water," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 376-380.
    7. Lai, Huilin & Ma, Changfeng, 2009. "Lattice Boltzmann method for the generalized Kuramoto–Sivashinsky equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1405-1412.

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