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Journal of Scientific Computing

Erschienen in:

22.08.2018

Error Estimates of Spectral Galerkin Methods for a Linear Fractional Reaction–Diffusion Equation

verfasst von: Zhongqiang Zhang

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2019

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Abstract

We consider a fractional diffusion equation with a reaction term in one dimensional space. We first establish the regularity in weighted Sobolev spaces. Then we present an optimal error estimate for a spectral Galerkin method for the equation and a sub-optimal error estimate for a spectral Petrov–Galerkin method. Numerical results suggest that the convergence order in a weighted \(L^2\)-norm is \(2\alpha +1\) for smooth inputs where \(\alpha \) is the order of the fractional Laplacian.

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Titel: Error Estimates of Spectral Galerkin Methods for a Linear Fractional Reaction–Diffusion Equation
verfasst von: Zhongqiang Zhang
Publikationsdatum: 22.08.2018
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0800-0

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