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Numerical Algorithms

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18-05-2019 | Original Paper

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

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

Published in: Numerical Algorithms | Issue 3/2020

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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
Publisher: Springer US
Published in: Numerical Algorithms / Issue 3/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-019-00722-w

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