Title: Some optimised schemes for 1D Korteweg-de-Vries equation

Authors: A.R. Appadu; M. Chapwanya; O.A. Jejeniwa

Addresses: Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa ' Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa ' Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

Abstract: Two new explicit finite difference schemes for the solution of the one-dimensional Korteweg-de-Vries equation are proposed. This equation describes the character of a wave generated by an incompressible fluid. We analyse the spectral properties of our schemes against two existing schemes proposed by Zabusky and Kruskal (1965) and Wang et al. (2008). An optimisation technique based on minimisation of the dispersion error is implemented to compute the optimal value of the spatial step size at a given value of the temporal step size and this is validated by some numerical experiments. The performance of the four methods are compared in regard to dispersive and dissipative errors and their ability to conserve mass, momentum and energy by using two numerical experiments which involve solitons.

Keywords: incompressible fluid; Korteweg-de-Vries; dissipation; dispersion; optimisation; solitons.

DOI: 10.1504/PCFD.2017.085177

Progress in Computational Fluid Dynamics, An International Journal, 2017 Vol.17 No.4, pp.250 - 266

Received: 03 Mar 2015
Accepted: 03 Mar 2016
Published online: 16 Jul 2017 *

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