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

Dylan Abrahamsen and Bengt Fornberg

Applied Mathematics and Computation, 2021, vol. 401, issue C

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.

Keywords: Hermite; Finite difference; Partial differential equations; KdV; Non-linear PDE (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:401:y:2021:i:c:s0096300321001491

DOI: 10.1016/j.amc.2021.126101

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