Convergence of an Embedded Exponential-Type Low-Regularity Integrators for the KdV Equation without Loss of Regularity  

作　　者：Yongsheng Li Yifei Wu Fangyan Yao 

机构地区：[1]School of Mathematical Sciences,South China University of Technology,Guangzhou,Guangdong 510640,China [2]Center for Applied Mathematics,Tianjin University,Tianjin 300072,China

出　　处：《Annals of Applied Mathematics》2021年第1期1-21,共21页应用数学年刊（英文版）

摘　　要：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,|<J^(γ)δx(fg),J^(γ)f>|■||f||H^(γ)^(2)||g||H^(γ+1),and replace f regularity.Based on these techniques,we prove that the ELRI scheme proposed in[41]provides 1/2-order convergence accuracy in H^(γ)for any initial data belonging to H^(γ)with γ>3/2,which does not require any additional derivative assumptions.

关 键 词：The KdV equation numerical solution convergence analysis error estimate low regularity fast Fourier transform 

分 类 号：O175[理学—数学]