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Journal of Applied Mathematics and Computing

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31.03.2018 | Original Research

Stability and convergence of a local discontinuous Galerkin method for the fractional diffusion equation with distributed order

verfasst von: Leilei Wei, Lijie Liu, Huixia Sun

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2019

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Abstract

In this paper, a numerical method is proposed for solving distributed order diffusion equation, which arises in the mathematical modeling of ultra-slow diffusion processes observed in some physical problems, whose solution decays logarithmically as the time t tends to infinity. Based on local discontinuous Galerkin method in space, we develop a fully discrete scheme and prove that the scheme is unconditionally stable and convergent with the order \(O(h^{k+1}+\Delta t+\Delta \alpha ^2)\), where \(h, \Delta t\),\(\Delta \alpha \) and k are the step size in space, time, distributed order and the degree of piecewise polynomials, respectively. Extensive numerical examples are carried out to illustrate the effectiveness of the numerical schemes.

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Titel: Stability and convergence of a local discontinuous Galerkin method for the fractional diffusion equation with distributed order
verfasst von: Leilei Wei
Lijie Liu
Huixia Sun
Publikationsdatum: 31.03.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2019
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-018-1182-z

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