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Padé numerical method for the Rosenau–Hyman compacton equation

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  • Rus, Francisco
  • Villatoro, Francisco R.

Abstract

Three implicit finite difference methods based on Padé approximations in space are developed for the Rosenau–Hyman K(n,n) equation. The analytical solutions and their invariants are used to assess the accuracy of these methods. Shocks which develop after the interaction of compactons are shown to be independent of the numerical method and its parameters indicating that their origin may not be numerical. The accuracy in long-time integrations of high-order Padé methods is shown.

Suggested Citation

  • Rus, Francisco & Villatoro, Francisco R., 2007. "Padé numerical method for the Rosenau–Hyman compacton equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(1), pages 188-192.
    • Handle: RePEc:eee:matcom:v:76:y:2007:i:1:p:188-192
    DOI: 10.1016/j.matcom.2007.01.016
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    References listed on IDEAS

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    1. Ismail, M.S. & Taha, T.R., 1998. "A numerical study of compactons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(6), pages 519-530.
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    Cited by:

    1. Hashemi, M.S., 2021. "A novel approach to find exact solutions of fractional evolution equations with non-singular kernel derivative," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Garralon-López, Rubén & Rus, Francisco & Villatoro, Francisco R., 2023. "Robustness of the absolute Rosenau–Hyman |K|(p,p) equation with non-integer p," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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