An Efficient Compact Difference Method for the Fourth-order Nonlocal Subdiffusion Problem

In this paper, a compact finite difference scheme is constructed and studied for the fourth-order subdiffusion equation with the Riemann–Liouville fractional integral. The Caputo time-fractional derivative term and the Riemann–Liouville fractional integral term are discretized by L1-2 discrete formula and second order convolution quadrature rule, respectively. By using the discrete energy method, the Cholesky decomposition method and the reduced-order method, the stability and convergence are attained. And the convergence orders are reached second-order in time and fourth-order in space. Numerical examples verify the theoretical analysis.