Year: 2018
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 764–781
Abstract
A finite difference method for a class of time-space fractional diffusion equations is considered. The trapezoidal formula and a fourth-order fractional compact difference scheme are, respectively, used in temporal and spatial discretisations and the method stability is studied. Theoretical estimates of the convergence in the $L_2$ -norm are shown to be $\mathscr{O}(τ^2+h^4)$, where $τ$ and $h$ are time and space mesh sizes. Numerical examples confirm theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.280218.210518
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 764–781
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Fractional diffusion equation Riesz derivative high-order approximation stability convergence.