Browsing by Author "Zhao, Yue"
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Article Citation Count: Arshad, Sadia...et al. (2018). "A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations", East Asian Journal on Applied Mathematics, Vol. 8, No. 4, pp. 764-781.A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations(Global Science Press, 2018) Arshad, Sadia; Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Zhao, Yue; 56389A 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 O(tau(2) + h(4)), where tau and h are time and space mesh sizes. Numerical examples confirm theoretical results.Article Citation Count: Arshad, Sadia...et al. (2018). Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative, Entropy, 20(5).Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative(MDPI, 2018) Arshad, Sadia; Baleanu, Dumitru; Huang, Jianfei; Al Qurashi, Maysaa Mohamed; Tang, Yifa; Zhao, Yue; 56389In this article, a numerical scheme is formulated and analysed to solve the time-space fractional advection-diffusion equation, where the Riesz derivative and the Caputo derivative are considered in spatial and temporal directions, respectively. The Riesz space derivative is approximated by the second-order fractional weighted and shifted Grunwald-Letnikov formula. Based on the equivalence between the fractional differential equation and the integral equation, we have transformed the fractional differential equation into an equivalent integral equation. Then, the integral is approximated by the trapezoidal formula. Further, the stability and convergence analysis are discussed rigorously. The resulting scheme is formally proved with the second order accuracy both in space and time. Numerical experiments are also presented to verify the theoretical analysis.
