A compact finite difference scheme for variable order subdiffusion equation. (English) Zbl 1524.65323
Summary: In this paper, we consider a variable order time subdiffusion equation. A Crank-Nicolson type compact finite difference scheme with second order temporal accuracy and fourth order spatial accuracy is presented. The stability and convergence of the scheme are strictly proved by using the discrete energy method. Finally, some numerical examples are provided, the results confirm the theoretical analysis and demonstrate the effectiveness of the compact difference method.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 26A33 | Fractional derivatives and integrals |
| 35R11 | Fractional partial differential equations |
Keywords:
fractional subdiffusion equation; variable order; compact finite difference scheme; stability and convergenceReferences:
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