@Article{AAM-37-1,
author = {Li , YongshengWu , Yifei and Yao , Fangyan},
title = {Convergence of  an Embedded Exponential-Type Low-Regularity Integrators for the KdV Equation  Without Loss of Regularity},
journal = {Annals of Applied Mathematics},
year = {2021},
volume = {37},
number = {1},
pages = {1--21},
abstract = {<p style="text-align: justify; margin-bottom: 10px;">In this paper, we study the convergence rate of an Embedded exponential-type low-regularity integrator (ELRI) for&nbsp; the&nbsp; Korteweg-de Vries equation. We develop some new harmonic analysis techniques to handle the &quot;stability&quot; issue. In particular, we use a new stability estimate which allows us to avoid the use of the fractional Leibniz inequality,<br/></p><p style="text-align: center; margin-bottom: 10px;"><img src="https://admin.global-sci.org/uploads/ueditor/image/20210223/1614068076263070.png" title="1614068076263070.png" alt="image.png"/></p><p style="text-align: justify; margin-bottom: 10px;"><span style="text-align: justify;">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 convergen</span><span style="text-align: justify;">ce accuracy&nbsp; in $H^\gamma$ for any initial data belonging to $H^\gamma$ with $\gamma &gt;\frac32$, which&nbsp; does not require any additional derivative assumptions.</span></p>},
issn = {},
doi = {https://doi.org/10.4208/aam.OA-2020-0001},
url = {http://global-sci.org/intro/article_detail/aam/18628.html}
}