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- Title
On a Multigrid Method for Tempered Fractional Diffusion Equations.
- Authors
Bu, Linlin; Oosterlee, Cornelis W.
- Abstract
In this paper, we develop a suitable multigrid iterative solution method for the numerical solution of second- and third-order discrete schemes for the tempered fractional diffusion equation. Our discretizations will be based on tempered weighted and shifted Grünwald difference (tempered-WSGD) operators in space and the Crank–Nicolson scheme in time. We will prove, and show numerically, that a classical multigrid method, based on direct coarse grid discretization and weighted Jacobi relaxation, performs highly satisfactory for this type of equation. We also employ the multigrid method to solve the second- and third-order discrete schemes for the tempered fractional Black–Scholes equation. Some numerical experiments are carried out to confirm accuracy and effectiveness of the proposed method.
- Subjects
MULTIGRID methods (Numerical analysis); HEAT equation; DISCRETIZATION methods; NUMERICAL analysis; JACOBI identity
- Publication
Fractal & Fractional, 2021, Vol 5, Issue 4, p145
- ISSN
2504-3110
- Publication type
Article
- DOI
10.3390/fractalfract5040145