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Convergence of an Embedded Exponential-Type Low-Regularity Integrators for the KdV Equation Without Loss of Regularity

Convergence of an Embedded Exponential-Type Low-Regularity Integrators for the KdV Equation Without Loss of Regularity
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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,

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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.

Author Details

Yongsheng Li

Yifei Wu

Fangyan Yao

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