A series of high-order quasi-compact schemes for space fractional diffusion equations based on the superconvergent approximations for fractional derivatives. (English) Zbl 1332.65131
The authors are concerned with some high-order quasi-compact schemes for space fractional diffusion equations. The approach relies on the superconvergence of the Grunvald approximation to the Riemann-Liouville derivative at a special point. The stability and convergence analysis is further investigated. Numerical experiments are presented that support the theoretical findings.
Reviewer: Marius Ghergu (Dublin)
MSC:
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35K05 | Heat equation |
| 35R11 | Fractional partial differential equations |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
fractional derivative; high-order scheme; quasi-compactness; stability; space fractional diffusion equations; superconvergence; convergence; numerical experimentSoftware:
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