The performance of a numerical scheme on the variable-order time-fractional advection-reaction-subdiffusion equations. (English) Zbl 07533815
Summary: 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 \(\alpha(\mathbf{x}, t) \in(0, 1)\). 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.
MSC:
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 35Rxx | Miscellaneous topics in partial differential equations |
| 35Kxx | Parabolic equations and parabolic systems |
Keywords:
variable-order time-fractional derivative; Grünwald formula; compact finite difference; reaction-subdiffusion problemReferences:
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