The performance of a numerical scheme on the variable-order time-fractional advection-reaction-subdiffusion equations

Abstract

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 α(x,t)∈(0,1). For the spatial and temporal discretization of the equation, a fourth-order compact finite difference operator and a third-order weighted-shifted Grünwald 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.