Browsing by Author "Kheirkhah, Farnaz"

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    The Performance of a Numerical Scheme on the Variable-Order Time-Fractional Advection-Reaction Equations
    (Elsevier, 2022) Hajipour, Mojtaba; Baleanu, Dumitru; Kheirkhah, Farnaz
    This paper is concerned with a highly accurate numerical scheme for a class of one and two-dimensional time-fractional advection-reaction-subdiffusion equations of variable order alpha(x, t) is an element of (0, 1). For the spatial and temporal discretization of the equation, a fourth order compact finite difference operator and a third-order weighted-shifted Grunwald formula are applied, respectively. The stability and convergence of the present scheme are addressed. Some extensive numerical experiments are performed to confirm the theoretical analysis and high-accuracy of this novel scheme. Comparisons are also made with the available schemes in the literature. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.