East Asian J. Appl. Math., 8 (2018), pp. 764-781.
Published online: 2018-10
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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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.280218.210518}, url = {http://global-sci.org/intro/article_detail/eajam/12818.html} }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.