TY - JOUR
AU1 - Chen, Hu
AU2 - Shi, Yanhua
AU3 - Zhang, Jiwei
AU4 - Zhao, Yanmin
AB - The sharp error estimate of a Grünwald–Letnikov (GL) scheme on uniform mesh for reaction-subdiffusion equations with weakly singular solutions is considered, where the spatial domain is a square in R2 which is discretized by Legendre Galerkin spectral method. A discrete fractional Grönwall inequality is shown by constructing a family of discrete complementary convolution (DCC) kernels for the discrete convolution coefficients of GL scheme, which is used to get the stability and convergence of the fully discrete scheme. By a delicate analysis of the convolution sum of DCC kernels and truncation errors, we also show that the error estimate is sharp and α-robust as the fractional order α→1−\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\alpha \rightarrow 1^{-}$\end{document}, which avoids the so-called coefficient blow-up phenomenon. Numerical examples are provided to verify the sharpness of our theoretical analysis.
TI - Sharp error estimate of a Grünwald–Letnikov scheme for reaction-subdiffusion equations
JF - Numerical Algorithms
DO - 10.1007/s11075-021-01161-2
DA - 2022-04-01
UR - https://www.deepdyve.com/lp/springer-journals/sharp-error-estimate-of-a-gr-nwald-letnikov-scheme-for-reaction-CXaFSJor6y
SP - 1465
EP - 1477
VL - 89
IS - 4
DP - DeepDyve
ER -