Convergence of an Embedded Exponential-Type Low-Regularity Integrators for the KdV Equation Without Loss of Regularity
Year: 2021
Author: Yongsheng Li, Yifei Wu, Fangyan Yao
Annals of Applied Mathematics, Vol. 37 (2021), Iss. 1 : pp. 1–21
Abstract
In this paper, we study the convergence rate of an Embedded exponential-type low-regularity integrator (ELRI) for the Korteweg-de Vries equation. We develop some new harmonic analysis techniques to handle the "stability" issue. In particular, we use a new stability estimate which allows us to avoid the use of the fractional Leibniz inequality,
and replace it by suitable inequalities without loss of regularity. Based on these techniques, we prove that the ELRI scheme proposed in [41] provides $\frac12$-order convergence accuracy in $H^\gamma$ for any initial data belonging to $H^\gamma$ with $\gamma >\frac32$, which does not require any additional derivative assumptions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2020-0001
Annals of Applied Mathematics, Vol. 37 (2021), Iss. 1 : pp. 1–21
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: The KdV equation numerical solution convergence analysis error estimate low regularity fast Fourier transform.
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