Second Order Compact Difference Scheme for Time Fractional Sub-diffusion Fourth-Order Neutral Delay Differential Equations

Abstract

In this paper, we propose a compact difference scheme of second order temporal convergence for the analysis of sub-diffusion fourth-order neutral fractional delay differential equations. In this regard, a difference scheme combining the compact difference operator for spatial discretization along with $$L2-1_{\sigma }$$ formula for Caputo fractional derivative is constructed and analyzed. Unique solvability, stability, and convergence of the proposed scheme are proved using the discrete energy method in $$L_2$$ norm. Established scheme is of second-order convergence in time and fourth-order convergence in spatial dimension, i.e., $$O(\tau ^{3-\alpha }+h^4)$$, where $$\tau$$ and h are time and space mesh sizes respectively and $$\alpha \in (0,1)$$. Finally, some numerical experiments are given to show the authenticity, efficiency, and accuracy of our theoretical results.