Second-order error analysis of the averaged L1 scheme (L1) for time-fractional initial-value and sub diffusion problems

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外文摘要：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(h2)convergence in space,where h is the spatial mesh width.Numerical experiments support our results.

外文关键词：

time-fractionalsubdiffusionaveraged L1 scheme

作者：

Jinye Shen、Fanhai Zeng、Martin Stynes

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作者单位：

School of Mathematics,Southwestern University of Finance and Economics,Chengdu 611130,China

School of Mathematics,Shandong University,Jinan 250100,China

Applied and Computational Mathematics Division,Beijing Computational Science Research Center,Beijing 100193,China

基金：

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaScience Foundation Program for Distinguished Young Scholars of Shandong(Overseas)

项目编号：

121015091217128312171025NSAF-U19304022022HWYQ-045

出版年：

2024

DOI：

10.1007/s11425-022-2078-4

中国科学:数学(英文版)

中国科学院

中国科学:数学(英文版)

CSTPCD

影响因子：0.36

ISSN：1674-7283

年,卷(期)：2024.67(7)