论文标题
在粗糙数据下，嵌入式指数型低指数积分器用于KDV方程
Embedded exponential-type low-regularity integrators for KdV equation under rough data
论文作者
论文摘要
在本文中，我们介绍了一类新型的嵌入式指数型低规范积分（ELRIS），用于求解KDV方程并在粗糙的初始数据下建立其最佳收敛结果。这些计划是明确和有效的。通过严格的错误分析，我们首先证明ELRI方案在$ H^γ$中提供了$ H^{γ+1} $的初始数据的第一阶准确性，对于$γ> \ frac12 $。此外，通过在第一阶方案中添加两个校正项，我们显示了一个二阶Elri，该阶级ELRI在$ h^γ$中提供$ H^{γ+3} $的第二阶准确性，以$ h^{γ+3} $，对于$γ\ ge0 $。拟议的Elris进一步减少了迄今为止现有方法的规律性要求，以实现最佳收敛。理论结果通过数值实验证实，与现有方法的比较说明了新方法的效率。
In this paper, we introduce a novel class of embedded exponential-type low-regularity integrators (ELRIs) for solving the KdV equation and establish their optimal convergence results under rough initial data. The schemes are explicit and efficient to implement. By rigorous error analysis, we first show that the ELRI scheme provides the first order accuracy in $H^γ$ for initial data in $H^{γ+1}$ for $γ>\frac12$. Moreover, by adding two more correction terms to the first order scheme, we show a second order ELRI that provides the second order accuracy in $H^γ$ for initial data in $H^{γ+3}$ for $γ\ge0$. The proposed ELRIs further reduce the regularity requirement of existing methods so far for optimal convergence. The theoretical results are confirmed by numerical experiments, and comparisons with existing methods illustrate the efficiency of the new methods.
