A compact difference scheme for fourth-order fractional sub-diffusion equations with Neumann boundary conditions

In this paper, a compact finite difference scheme with global convergence order $O(\tau^{2}+h^4)$ is derived for fourth-order fractional sub-diffusion equations subject to Neumann boundary conditions. The difficulty caused by the fourth-order derivative and Neumann boundary conditions is carefully handled. The stability and convergence of the proposed scheme are studied by the energy method. Theoretical results are supported by numerical experiments.