Stability and Time-Step Constraints of Implicit-Explicit Runge-Kutta Methods for the Linearized Korteweg-de Vries Equation  

作　　者：Joseph Hunter Zheng Sun Yulong Xing 

机构地区：[1]Department of Mathematics,The Ohio State University,Columbus,OH,43210,USA [2]Department of Mathematics,The University of Alabama,Tuscaloosa,AL,35487,USA

出　　处：《Communications on Applied Mathematics and Computation》2024年第1期658-687,共30页应用数学与计算数学学报（英文）

基　　金：supported by the NSF under Grant DMS-2208391;sponsored by the NSF under Grant DMS-1753581.

摘　　要：This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.

关 键 词：Linearized Korteweg-de Vries(KdV)equation Implicit-explicit(IMEX)Runge-Kutta(RK)method STABILITY Courant-Friedrichs-Lewy(CFL)condition Finite difference(FD)method Local discontinuous Galerkin(DG)method 

分 类 号：O17[理学—数学]