Chen, Jinghua; Chen, Xuejuan; Zhang, Hongmei Numerical simulation of two-dimensional tempered fractional diffusion equation. (Chinese. English summary) Zbl 1449.65174 J. Xiamen Univ., Nat. Sci. 58, No. 6, 882-888 (2019). 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 Keywords:tempered fractional derivative; alternating direction implicit method; Crank-Nicolson scheme PDFBibTeX XMLCite \textit{J. Chen} et al., J. Xiamen Univ., Nat. Sci. 58, No. 6, 882--888 (2019; Zbl 1449.65174) Full Text: DOI