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18-05-2019 | Original Paper | Issue 3/2020

Sharp H¹-norm error estimate of a cosine pseudo-spectral scheme for 2D reaction-subdiffusion equations

Journal:: Numerical Algorithms > Issue 3/2020

Authors:: Xin Li, Luming Zhang, Hong-lin Liao

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Abstract

A finite difference cosine pseudo-spectral scheme is presented for solving a linear reaction-subdiffusion problem with Neumann boundary conditions. The nonuniform version of L1 formula is employed for approximating the Caputo fractional derivative, and a cosine pseudo-spectral approximation is utilized in spatial discretization. With the help of discrete fractional Grönwall inequality and global consistency analysis, sharp H¹-norm error estimate reflecting the regularity of solution is verified for the proposed method. A fast algorithm is implemented in computation and numerical results confirm the sharpness of our analysis.

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Title: Sharp H1-norm error estimate of a cosine pseudo-spectral scheme for 2D reaction-subdiffusion equations
Authors:: Xin Li
Luming Zhang
Hong-lin Liao
Publication date: 18-05-2019
DOI: https://doi.org/10.1007/s11075-019-00722-w
Publisher: Springer US
Journal: Numerical Algorithms
Issue 3/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265

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