On time relaxed schemes and formulations for dispersive wave equations

AIMS Mathematics. 2019;4(2):254-278 DOI 10.3934/math.2019.2.254

 

Journal Homepage

Journal Title: AIMS Mathematics

ISSN: 2473-6988 (Online)

Publisher: AIMS Press

LCC Subject Category: Science: Mathematics

Country of publisher: United States

Language of fulltext: English

Full-text formats available: PDF, HTML

 

AUTHORS


Jean-Paul Chehab (1 Université de Picardie Jules Verne, LAMFA CNRS UMR 7352, 33, rue Saint-Leu, 80039 Amiens, France)

Denys Dutykh (2 Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA, 73000 Chambéry, France)

EDITORIAL INFORMATION

Blind peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 14 weeks

 

Abstract | Full Text

The numerical simulation of nonlinear dispersive waves is a central research topic of many investigations in the nonlinear wave community. Simple and robust solvers are needed for numerical studies of water waves as well. The main diFFIculties arise in the numerical approximation of high order derivatives and in severe stability restrictions on the time step, when explicit schemes are used. In this study we propose new relaxed system formulations which approximate the initial dispersive wave equation. However, the resulting relaxed system involves first order derivatives only and it is written in the form of an evolution problem. Thus, many standard methods can be applied to solve the relaxed problem numerically. In this article we illustrate the application of the new relaxed scheme on the classical Korteweg–de Vries equation as a prototype of stiFF dispersive PDEs.