Kheirkhah, FarnazHajipour, MojtabaBaleanu, DumitruMatematik2024-05-142024-05-142022Kheirkhah, Farnaz; Hajipour, Mojtaba; Baleanu, D. (2022). "The performance of a numerical scheme on the variable-order time-fractional advection-reaction-subdiffusion equations", Applied Numerical Mathematics, Vol.178, pp.25-40.0168-92741873-5460https://doi.org/10.1016/j.apnum.2022.03.016Hajipour, Mojtaba/0000-0002-7223-9577This 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.eninfo:eu-repo/semantics/closedAccessVariable-Order Time-Fractional DerivativeGrunwald FormulaCompact Finite DifferenceReaction-Subdiffusion ProblemArticle178254010.1016/j.apnum.2022.03.0162-s2.0-85127208702WOS:000790509900002Q1Q1