A Novel Error Analysis of Spectral Method for the Anomalous Subdiffusion Problems with Multi-term Time-fractional Derivative  

作　　者：Bo TANG Yan-ping CHEN Bin XIE Xiu-xiu LIN 

机构地区：[1]School of Mathematical Sciences,South China Normal University,Guangzhou,520631,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第4期943-961,共19页应用数学学报（英文版）

基　　金：supported by the State Key Program of National Natural Science Foundation of China(Nos.11931003);National Natural Science Foundation of China(Nos.41974133)。

摘　　要：This paper aims to extend a space-time spectral method to address the multi-term time-fractional subdiffusion equations with Caputo derivative. In this method, the Jacobi polynomials are adopted as the basis functions for temporal discretization and the Lagrangian polynomials are used for spatial discretization. An efficient spectral approximation of the weak solution is established. The main work is the demonstration of the well-posedness for the weak problem and the derivation of a posteriori error estimates for the spectral Galerkin approximation. Extensive numerical experiments are presented to perform the validity of a posteriori error estimators, which support our theoretical results.

关 键 词：space-time spectral methods multi-term time-fractional WELL-POSEDNESS a posteriori error estimates 

分 类 号：O241.8[理学—计算数学]