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Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation

Author

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  • Zakieh Avazzadeh

    (Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
    Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Vietnam)

  • Omid Nikan

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran)

  • José A. Tenreiro Machado

    (Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, 4249-015 Porto, Portugal)

Abstract

This paper investigates the solitary wave solutions of the generalized Rosenau–Korteweg-de Vries-regularized-long wave equation. This model is obtained by coupling the Rosenau–Korteweg-de Vries and Rosenau-regularized-long wave equations. The solution of the equation is approximated by a local meshless technique called radial basis function (RBF) and the finite-difference (FD) method. The association of the two techniques leads to a meshless algorithm that does not requires the linearization of the nonlinear terms. First, the partial differential equation is transformed into a system of ordinary differential equations (ODEs) using radial kernels. Then, the ODE system is solved by means of an ODE solver of higher-order. It is shown that the proposed method is stable. In order to illustrate the validity and the efficiency of the technique, five problems are tested and the results compared with those provided by other schemes.

Suggested Citation

  • Zakieh Avazzadeh & Omid Nikan & José A. Tenreiro Machado, 2020. "Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation," Mathematics, MDPI, vol. 8(9), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1601-:d:414851
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    References listed on IDEAS

    as
    1. Jinsong Hu & Yulan Wang, 2013. "A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-8, November.
    2. Maobo Zheng & Jun Zhou, 2014. "An Average Linear Difference Scheme for the Generalized Rosenau-KdV Equation," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, February.
    3. Su, LingDe, 2019. "A radial basis function (RBF)-finite difference (FD) method for the backward heat conduction problem," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 232-247.
    4. Jinsong Hu & Youcai Xu & Bing Hu, 2013. "Conservative Linear Difference Scheme for Rosenau-KdV Equation," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-7, April.
    5. Xintian Pan & Luming Zhang, 2012. "Numerical Simulation for General Rosenau-RLW Equation: An Average Linearized Conservative Scheme," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-15, May.
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