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Solitary-wave solutions of the GRLW equation using septic B-spline collocation method

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  • Karakoç, S. Battal Gazi
  • Zeybek, Halil

Abstract

In this work, solitary-wave solutions of the generalized regularized long wave (GRLW) equation are obtained by using septic B-spline collocation method with two different linearization techniques. To demonstrate the accuracy and efficiency of the numerical scheme, three test problems are studied by calculating the error norms L2 and L∞ and the invariants I1, I2 and I3. A linear stability analysis based on the von Neumann method of the numerical scheme is also investigated. Consequently, our findings indicate that our numerical scheme is preferable to some recent numerical schemes.

Suggested Citation

  • Karakoç, S. Battal Gazi & Zeybek, Halil, 2016. "Solitary-wave solutions of the GRLW equation using septic B-spline collocation method," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 159-171.
    • Handle: RePEc:eee:apmaco:v:289:y:2016:i:c:p:159-171
    DOI: 10.1016/j.amc.2016.05.021
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    References listed on IDEAS

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    1. Dumbser, M. & Facchini, M., 2016. "A space-time discontinuous Galerkin method for Boussinesq-type equations," Applied Mathematics and Computation, Elsevier, vol. 272(P2), pages 336-346.
    2. Hammad, D.A. & El-Azab, M.S., 2015. "A 2N order compact finite difference method for solving the generalized regularized long wave (GRLW) equation," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 248-261.
    3. Soliman, A.A., 2005. "Numerical simulation of the generalized regularized long wave equation by He’s variational iteration method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(2), pages 119-124.
    4. Hamdi, S. & Enright, W.H. & Schiesser, W.E & Gottlieb, J.J., 2004. "Exact solutions and invariants of motion for general types of regularized long wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(4), pages 535-545.
    5. Hammad, D.A. & El-Azab, M.S., 2015. "2N order compact finite difference scheme with collocation method for solving the generalized Burger’s–Huxley and Burger’s–Fisher equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 296-311.
    6. Ramos, J.I., 2007. "Solitary wave interactions of the GRLW equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 479-491.
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