A Lawson-type exponential integrator for the Korteweg-de Vries equation

2018/07/12 by Ostermann, Alexander, Su, Chunmei · 1 citation
#65M15 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1807.04570

Abstract

We propose an explicit numerical method for the periodic Korteweg-de Vries equation. Our method is based on a Lawson-type exponential integrator for time integration and the Rusanov scheme for Burgers' nonlinearity. We prove first-order convergence in both space and time under a mild Courant-Friedrichs-Lewy condition τ=O(h), where τ and h represent the time step and mesh size, respectively. Numerical examples illustrating our convergence result are given.

Cited by

• Computing rough solutions of the KdV equation below \bf L²

Related

• An exponential-type integrator for the KdV equation
• Convergence error estimates at low regularity for time discretizations of KdV
• Notes on a high order fully discrete scheme for the Korteweg-de vries equation with a time-stepping procedure of Runge-Kutta-composition type
• Rough solutions for the periodic Korteweg-de Vries equation
• Long-time asymptotic behavior for an extended modified Korteweg-de Vries equation