Temporal Second-order Scheme for a Hidden-memory Variable Order Time Fractional Diffusion Equation with an Initial Singularity  

作　　者：Rui-lian DU Zhi-zhong SUN 

机构地区：[1]School of Big Data,Changzhou University,Changzhou 213164,China [2]Department of Mathematics,Shanghai University,Shanghai 200444,China [3]School of Mathematics,Southeast University,Nanjing 210096,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第4期1060-1077,共18页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.12201076);the China Postdoctoral Science Foundation(No.2023M732180)。

摘　　要：In this work,a novel time-stepping L1 formula is developed for a hidden-memory variable-order Caputo’s fractional derivative with an initial singularity.This formula can obtain second-order accuracy and an error estimate is analyzed strictly.As an application,a fully discrete difference scheme is established for the initial-boundary value problem of a hidden-memory variable-order time fractional diffusion model.Numerical experiments are provided to support our theoretical results.

关 键 词：time fractional diffusion equation hidden-memory variable-order fractional derivative error estimate initial singularity 

分 类 号：O241.8[理学—计算数学]