Block-centered finite difference method for a tempered subdiffusion model with time-dependent coefficients. (English) Zbl 1538.65247
Summary: In this paper, the block-centered finite difference method with two kinds of tempered \(L1\) discretizations is introduced for a tempered subdiffusion model with time-dependent coefficients. The present numerical schemes are constructed by using the implicit tempered \(L1\) discretization and the implicit-explicit tempered \(L1\) discretization to approximate the tempered Caputo fractional derivative in the temporal direction and using the block-centered finite difference method to approximate derivatives in the spatial direction. The stability and convergence of the present difference schemes on non-uniform grids for one- and two-dimensional tempered subdiffusion problems are proved. The theoretical analysis shows that the present numerical schemes give the optimal convergence rates for both temporal and spatial variables. Extensive numerical examples are given to verify the theoretical results.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35M30 | Mixed-type systems of PDEs |
| 26A33 | Fractional derivatives and integrals |
Keywords:
tempered subdiffusion model; block-centered finite difference; tempered \(L1\) discretization; graded mesh; error estimateSoftware:
Adaptative L1 TE and PredictiveReferences:
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