发表机构
Indian Institute of Technology Kanpur; University of Catania; King Abdullah University of Science and Technology（坎普尔印度理工学院; 卡塔尼亚大学; 阿卜杜拉国王科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究指数时间积分与傅里叶伪谱离散化用于双曲KdV系统，证明ETD方法渐近保持而Lawson方法不满足，并提出高效实现，与ImEx Runge-Kutta相比具竞争力。
AI 中文摘要
我们研究了将指数时间积分方法与傅里叶伪谱空间离散化相结合，应用于双曲Korteweg-de Vries（KdVH）系统。我们研究了此类离散化的渐近保持（AP）性质，表明一般而言，Lawson方法不是渐近保持的，因为辅助（导数逼近）变量不满足极限平衡流形，而指数时间差分（ETD）方法对所有分量（包括解变量和辅助变量）都是AP的。我们还提出了一种基于该系统矩阵指数精确公式的高效数值实现，并将其与先前提出的ImEx Runge-Kutta时间积分方法进行比较，表明指数方法在此背景下具有竞争力。
英文摘要
We study the application of exponential time integration methods, coupled with Fourier pseudospectral space discretization, to the hyperbolic Korteweg-de Vries (KdVH) system. We investigate the asymptotic preserving (AP) properties of such discretizations, showing that, in general, Lawson methods are not asymptotic preserving, because the auxiliary (derivative-approximating) variables do not satisfy the limit equilibrium manifold, whereas exponential time differencing (ETD) methods are AP for all components, including both the solution variable and the auxiliary variables. We also present an efficient numerical implementation based on an exact formula for the matrix exponential of this system, and compare it with previously-proposed ImEx Runge-Kutta time integration, showing that exponential methods can be competitive in this context.
