Second-order error analysis of the averaged L1 scheme L1 for time-fractional initial-value and subdiffusion problems  

作　　者：Jinye Shen Fanhai Zeng Martin Stynes 

机构地区：[1]School of Mathematics,Southwestern University of Finance and Economics,Chengdu,611130,China [2]School of Mathematics,Shandong University,Jinan,250100,China [3]Applied and Computational Mathematics Division,Beijing Computational Science Research Center,Beijing,100193,China

出　　处：《Science China Mathematics》2024年第7期1641-1664,共24页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 12101509, 12171283, 12171025 and NSAF-U1930402);the Science Foundation Program for Distinguished Young Scholars of Shandong (Overseas) (Grant No. 2022HWYQ-045)。

摘　　要：Fractional initial-value problems(IVPs) and time-fractional initial-boundary value problems(IBVPs), each with a Caputo temporal derivative of order α ∈(0, 1), are considered. An averaged variant of the well-known L1 scheme is proved to be O(N^(-2)) convergent for IVPs on suitably graded meshes with N points, thereby improving the O(N^(-(2-α))) convergence rate of the standard L1 scheme. The analysis relies on a delicate decomposition of the temporal truncation error that yields a sharp dependence of the order of convergence on the degree of mesh grading used. This averaged L1 scheme can be combined with a finite difference or piecewise linear finite element discretization in space for IBVPs, and under a restriction on the temporal mesh width, one gets again O(N^(-2)) convergence in time, together with O(h^(2)) convergence in space,where h is the spatial mesh width. Numerical experiments support our results.

关 键 词：time-fractional SUBDIFFUSION averaged L1 scheme 

分 类 号：O175.8[理学—数学]