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On the solution of time-fractional KdV–Burgers equation using Petrov–Galerkin method for propagation of long wave in shallow water

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  • Gupta, A.K.
  • Ray, S. Saha

Abstract

In the present article, Petrov–Galerkin method has been utilized for the numerical solution of nonlinear time-fractional KdV–Burgers (KdVB) equation. The nonlinear KdV–Burgers equation has been solved numerically through the Petrov–Galerkin approach utilising a quintic B-spline function as the trial function and a linear hat function as the test function . The numerical outcomes are observed in good agreement with exact solutions for classical order. In case of fractional order, the numerical results of KdV–Burgers equations are compared with those obtained by new method proposed in [1]. Numerical experiments exhibit the accuracy and efficiency of the approach in order to solve nonlinear dispersive and dissipative problems like the time-fractional KdV–Burgers equation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:376-380
    DOI: 10.1016/j.chaos.2018.09.046
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    References listed on IDEAS

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    1. 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.
    2. Seyma Tuluce Demiray & Yusuf Pandir & Hasan Bulut, 2014. "Generalized Kudryashov Method for Time-Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, July.
    3. Wang, Qi, 2008. "Homotopy perturbation method for fractional KdV-Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 843-850.
    4. Odibat, Zaid M., 2009. "Exact solitary solutions for variants of the KdV equations with fractional time derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1264-1270.
    5. Gupta, A.K. & Saha Ray, S., 2017. "On the solitary wave solution of fractional Kudryashov–Sinelshchikov equation describing nonlinear wave processes in a liquid containing gas bubbles," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 1-12.
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    Cited by:

    1. Kudryashov, Nikolay A., 2021. "Generalized Hermite polynomials for the Burgers hierarchy and point vortices," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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    Keywords

    26A33; 35G25; 35R11; 35Q35; 42C40;
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