TY - JOUR T1 - Convergence of an Embedded Exponential-Type Low-Regularity Integrators for the KdV Equation Without Loss of Regularity AU - Li , Yongsheng AU - Wu , Yifei AU - Yao , Fangyan JO - Annals of Applied Mathematics VL - 1 SP - 1 EP - 21 PY - 2021 DA - 2021/02 SN - 37 DO - http://doi.org/10.4208/aam.OA-2020-0001 UR - https://global-sci.org/intro/article_detail/aam/18628.html KW - The KdV equation, numerical solution, convergence analysis, error estimate, low regularity, fast Fourier transform. AB -

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.