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Yuste, S.B. and Acedo, L. (2005) An Explicit Finite Difference Method and a New Von Neumann-Type Stability Analysis for Fractional Diffusion Equations. SIAM Journal on Numerical Analysis, 42, 1862-1874.
https://doi.org/10.1137/030602666

has been cited by the following article:

• TITLE: A Compact Finite Volume Scheme for the Multi-Term Time Fractional Sub-Diffusion Equation

  AUTHORS: Baojin Su, Yanan Wang, Jingwen Qi, Yousen Li

  KEYWORDS: Multi-Term Time Fractional Sub-Diffusion Equation, High-Order Compact Finite Volume Scheme, Stable, Convergent

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.10, October 27, 2022

  ABSTRACT: In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obtain the compact finite volume scheme have high order accuracy. We use a compact operator to deal with spatial direction; then we can get the compact finite volume scheme. It is proved that the finite volume scheme is unconditionally stable and convergent in L∞-norm. The convergence order is O(τ2-α + h4). Finally, two numerical examples are given to confirm the theoretical results. Some tables listed also can explain the stability and convergence of the scheme.