Zhang, Q.F., Ran, M.H. and Xu, D.H. (2017) Analysis of the Compact Difference Scheme for the Semilinear Fractional Partial Differential Equation with Time Delay. Applicable Analysis, 96, 1867-1884.
https://doi.org/10.1080/00036811.2016.1197914

has been cited by the following article:

• TITLE: Compact Difference Method for Time-Fractional Neutral Delay Nonlinear Fourth-Order Equation

  AUTHORS: Huan Wang, Qing Yang

  KEYWORDS: Two-Dimensional Nonlinear Sub-Diffusion Equations, Neutral Delay, Compact Difference Scheme, Convergence, Stability

  JOURNAL NAME: Engineering, Vol.14 No.12, December 29, 2022

  ABSTRACT: In this paper, we present a compact finite difference method for a class of fourth-order nonlinear neutral delay sub-diffusion equations in two-dimensional space. The fourth-order problem is first transformed into a second-order system by a reduced-order method. Next by using compact operator to approximate the second order space derivatives and L2-1σ formula to approximate the time fractional derivative, the difference scheme which is fourth order in space and second order in time is obtained. Then, the existence and uniqueness of solution, the convergence rate of and the stability of the scheme are proved. Finally, numerical results are given to verify the accuracy and validity of the scheme.