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Chebyshev–Chebyshev spectral collocation method for solving the generalized regularized long wave (GRLW) equation

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  • Hammad, D.A.
  • El-Azab, M.S.

Abstract

In this research, a Chebyshev–Chebyshev spectral collocation method based on Kronecker and Hadamard products is proposed for solving the generalized regularized long wave (GRLW) equation. Chebyshev–Gauss–Lobatto collocation points are used in both time and space directions. Three invariants of motion: mass, momentum and energy are evaluated to determine the conservation properties of the GRLW equation. The single solitary wave and the interaction of two and three solitary waves are presented to validate the efficiency and the accuracy of the proposed scheme.

Suggested Citation

  • Hammad, D.A. & El-Azab, M.S., 2016. "Chebyshev–Chebyshev spectral collocation method for solving the generalized regularized long wave (GRLW) equation," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 228-240.
    • Handle: RePEc:eee:apmaco:v:285:y:2016:i:c:p:228-240
    DOI: 10.1016/j.amc.2016.03.033
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    References listed on IDEAS

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    1. 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.
    2. El-Danaf, Talaat S. & Ramadan, Mohamed A. & Abd Alaal, Faysal E.I., 2005. "The use of adomian decomposition method for solving the regularized long-wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 747-757.
    3. Raslan, K.R., 2009. "Numerical study of the Modified Regularized Long Wave (MRLW) equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1845-1853.
    4. 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.
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    Cited by:

    1. Fuchang Zheng & Shuhong Bao & Yulan Wang & Shuguang Li & Zhiyuan Li, 2017. "A Good Numerical Method for the Solution of Generalized Regularized Long Wave Equation," Modern Applied Science, Canadian Center of Science and Education, vol. 11(6), pages 1-72, June.
    2. Yu, Hao & Wu, Boying & Zhang, Dazhi, 2018. "A generalized Laguerre spectral Petrov–Galerkin method for the time-fractional subdiffusion equation on the semi-infinite domain," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 96-111.

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