REGULARITY THEORY AND NUMERICAL ALGORITHM FOR THE TIME-FRACTIONAL KLEIN-KRAMERS EQUATION  

作　　者：Jing Sun Daxin Nie Weihua Deng 

机构地区：[1]School of Mathematics and Statistics,Gansu Key Laboratory of Applied Mathematics and Complex Systems,Lanzhou University,Lanzhou 730000,China

出　　处：《Journal of Computational Mathematics》2025年第2期257-279,共23页计算数学(英文)

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12201270,12071195,12225107);by the Innovative Groups of Basic Research in Gansu Province(Grant No.22JR5RA391);by the Science and Technology Plan of Gansu Province(Grant No.22JR5RA535);by the Major Science and Technology Projects in Gansu Province-Leading Talents in Science and Technology(Grant No.23ZDKA0005);by the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2022-pd04);by the China Postdoctoral Science Foundation(Grant No.2022M721439).

摘　　要：Fractional Klein-Kramers equation can well describe subdiffusion in phase space.In this paper,we develop the fully discrete scheme for time-fractional Klein-Kramers equation based on the backward Euler convolution quadrature and local discontinuous Galerkin methods.Thanks to the obtained sharp regularity estimates in temporal and spatial directions after overcoming the hypocoercivity of the operator,the complete error analyses of the fully discrete scheme are built.It is worth mentioning that the convergence of the provided scheme is independent of the temporal regularity of the exact solution.Finally,numerical results are proposed to verify the correctness of the theoretical results.

关 键 词：Time-fractional Klein-Kramers equation Regularity estimate Convolution quadrature Local discontinuous Galerkin method Error analysis 

分 类 号：O17[理学—数学]