文献类型：期刊文献

英文题名：Sharp H-1-norm error estimates of two time-stepping schemes for reaction-subdiffusion problems

作者：Ren, Jincheng[1];Liao, Hong-lin[2];Zhang, Jiwei[3,4];Zhang, Zhimin[5,6]

通讯作者：Liao, HL[1]

机构：[1]Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou 450046, Peoples R China;[2]Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211106, Peoples R China;[3]Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China;[4]Wuhan Univ, Hubei Key Lab Computat Sci, Wuhan 430072, Peoples R China;[5]Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China;[6]Wayne State Univ, Dept Math, Detroit, MI 48202 USA

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211106, Peoples R China.

年份：2021

卷号：389

外文期刊名：JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000614704900019)】；

基金：This author is supported in part by NSFC, PR China grant 11601119, the program No. 18HASTIT027 for HASTIT, PR China, and Young talents Fund of HUEL.; This author is supported in part by NSFC grant 12071216, the grant 1008-56SYAH18037 from NUAA Scientific Research, PR China Starting Fund of Introduced Talent, and a grant DRA2015518 from 333 High-level Personal Training Project of Jiangsu Province, PR China.; This author is supported in part by NSFC, PR China grants 11771035 and NSAF, PR China U1930402, the Natural Science Foundation of Hubei Province, PR China No. 2019CFA007, and Xiangtan University, PR China 2018ICIP01.; This author is supported in part by NSFC, PR China grants 11871092, 11926356, and NSAF, PR China U1930402.

语种：英文

外文关键词：Reaction-subdiffusion problems; Initial singularity; Discrete Gronwall inequality; Time-space error-splitting technique; Sharp H-1-norm error estimate

摘要：Due to the intrinsically initial singularity of solution and the discrete convolution form in numerical Caputo derivatives, the traditional H-1-norm analysis (corresponding to the case for a classical diffusion equation) to the time approximations of a fractional subdiffusion problem always leads to suboptimal error estimates (a loss of time accuracy). To recover the theoretical accuracy in time, we propose an improved discrete Gronwall inequality and apply it to the well-known L1 formula and a fractional Crank-Nicolson scheme. With the help of a time-space error-splitting technique and the global consistency analysis, sharp H-1-norm error estimates of the two nonuniform approaches are established for a reaction-subdiffusion problems. Numerical experiments are included to confirm the sharpness of our analysis. (C) 2020 Elsevier B.V. All rights reserved.