@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 = {

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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2020-0001}, url = {http://global-sci.org/intro/article_detail/aam/18628.html} }