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Numerical study of the Modified Regularized Long Wave (MRLW) equation

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  • Raslan, K.R.

Abstract

The quadratic B-spline functions and the central difference operator for the time derivative have been used to develop a new algorithm based on the collocation method to solve modified regularized long wave equation. A linear stability analysis of the scheme is shown to be marginally stable. The method is validated by studying solitary wave motion, two and three solitary wave interaction, the evolution of solitary waves, and undular bore development.

Suggested Citation

  • Raslan, K.R., 2009. "Numerical study of the Modified Regularized Long Wave (MRLW) equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1845-1853.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1845-1853
    DOI: 10.1016/j.chaos.2009.03.098
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    References listed on IDEAS

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    1. Lu, Junfeng, 2009. "He’s variational iteration method for the modified equal width equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2102-2109.
    2. Ramos, J.I., 2007. "Solitary waves of the EW and RLW equations," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1498-1518.
    3. 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.
    4. Soliman, A.A. & Abdou, M.A., 2007. "Exact travelling wave solutions of nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 808-815.
    5. 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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    Cited by:

    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. Gao, Yali & Mei, Liquan, 2015. "Mixed Galerkin finite element methods for modified regularized long wave equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 267-281.
    3. 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.
    4. Li, Qi & Mei, Liquan, 2018. "Local momentum-preserving algorithms for the GRLW equation," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 77-92.

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