A Lawson-type exponential integrator for the Korteweg–de Vries equation. (16th October 2019)

• Record Type: Journal Article
• Authors: Ostermann, Alexander; Su, Chunmei
• Is Part Of: IMA journal of numerical analysis. Volume 40:Number 4(2020)
• Page Start: 2399
• Page End: 2414
• Publication Date: 2019-10-16
• Subjects: exponential integrators -- Lawson methods -- Korteweg–de Vries equation -- error estimates -- Rusanov scheme; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drz030
• Languages: English
• ISSNs: 0272-4979

Abstract

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 $\tau =O(h)$, where $\tau$ and $h$ represent the time step and mesh size for solutions in the Sobolev space $H^3((-\pi, \pi ))$, respectively. Numerical examples illustrating our convergence result are given.