Notes on a high order fully discrete scheme for the Korteweg-de vries equation with a time-stepping procedure of Runge-Kutta-composition type

2020/05/26 by Vassilios A. Dougalis, Dougalis, Vassilios A., A. Durán +1 · 3 citations
Mathematics · Engineering · #Numerical methods for differential equations #Electromagnetic Simulation and Numerical Methods #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.2005.12955

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 L² error estimates for the resulting semidiscrete and the fully discrete approximations.

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• A high-order method for the numerical approximation of fractional nonlinear Schrödinger equations
• Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schrödinger equations
• Solitary-wave solutions of the fractional nonlinear Schrödinger equation. II. A numerical study of the dynamics

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