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Numerical simulation of two-dimensional tempered fractional diffusion equation. (Chinese. English summary) Zbl 1449.65174

Summary: This paper discusses a two-dimensional tempered fractional diffusion equation, in which the tempered fractional derivative is the extension of fractional derivative. The scheme can model the transition from super-diffusion early time to diffusive late-time behavior. We apply the alternating directions implicit approach and the Crank-Nicolson (C-N) algorithm to establish our numerical discretization scheme. Furthermore, we obtain the second-order accurate difference method by a Richardson extrapolation. The stability and the convergence of the numerical scheme are proven via the technique of matrix analysis. A numerical example is given to demonstrate the efficiency of the designed schemes.

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
35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
65B05 Extrapolation to the limit, deferred corrections
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