A high-order fully discrete scheme for the Korteweg–de Vries equation with a time-stepping procedure of Runge–Kutta-composition type-Reference-Cited by-同舟云学术

A high-order fully discrete scheme for the Korteweg–de Vries equation with a time-stepping procedure of Runge–Kutta-composition type

Published:2021-08-12 Issue: Volume: Page:
ISSN:0272-4979
Container-title:IMA Journal of Numerical Analysis
language:en
Short-container-title:

Author:

Dougalis Vassilios A¹²,Durán Ángel³

Affiliation:

1. Mathematics Department, University of Athens, 15784 Zographou, Greece, and

2. Institute of Applied and Computational Mathematics, Foundation for Research and Technology Hellas (IACM-FORTH), 71110 Heraklion, Greece

3. Applied Mathematics Department, University of Valladolid, and Institute of Mathematics of the University of Valladolid (IMUVA), Paseo de Belén S/N, 47011 Valladolid, Spain

Abstract

Abstract We consider the periodic initial-value problem for the Korteweg–de Vries equation that we discretize in space by a spectral Fourier–Galerkin method and in time by an implicit, high-order, Runge–Kutta scheme of composition type based on the implicit midpoint rule. We prove $L^{2}$ error estimates for the resulting semidiscrete and the fully discrete approximations. Some numerical experiments illustrate the results.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Mathematics,General Mathematics

Link

http://academic.oup.com/imajna/advance-article-pdf/doi/10.1093/imanum/drab060/39733966/drab060.pdf

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