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Solving the Korteweg-de Vries equation with Hermite-based finite differences

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  • Abrahamsen, Dylan
  • Fornberg, Bengt

Abstract

The Korteweg-de Vries (KdV) equation is extensively studied in the field of nonlinear waves, with one key tool for this being fast and accurate numerical algorithms. Finite difference (FD) and pseudo-spectral (PS) methods are commonly used. We discuss here the pros and cons in this application area for a new class of Hermite-based finite difference (HFD) methods. Their most notable characteristic is to remain more ‘local’ than FD approximations for increasing orders of accuracy, translating into smaller error constants.

Suggested Citation

  • Abrahamsen, Dylan & Fornberg, Bengt, 2021. "Solving the Korteweg-de Vries equation with Hermite-based finite differences," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    • Handle: RePEc:eee:apmaco:v:401:y:2021:i:c:s0096300321001491
    DOI: 10.1016/j.amc.2021.126101
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    Cited by:

    1. Chinonso Nwankwo & Weizhong Dai & Tony Ware, 2023. "Enhancing accuracy for solving American CEV model with high-order compact scheme and adaptive time stepping," Papers 2309.03984, arXiv.org, revised Sep 2023.

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