2019/06/02 by Yu Fan, Yu, Fan, Minghua Chen +1
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1906.00328
openalex publication_date 2019/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main contribution of this work is to construct and analyze stable and high order schemes to efficiently solve the two-dimensional time Caputo-Fabrizio fractional diffusion equation. Based on a third-order finite difference method in time and spectral methods in space, the proposed scheme is unconditionally stable and has the global truncation error O(τ3+N-m), where τ, N and m are the time step size, polynomial degree and regularity in the space variable of the exact solution, respectively. It should be noted that the global truncation error O(τ2+N-m) is well established in [ Li, Lv and Xu, \em Numer. Methods Partial Differ. Equ. (2019)]. Finally, some numerical experiments are carried out to verify the theoretical analysis. To the best of our knowledge, this is the first proof for the stability of the third-order scheme for the Caputo-Fabrizio fractional operator.