An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations

Abstract EN

In this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation.

A numerical scheme for the equation has been derived to obtain 2-α in time and fourth-order in space.

We improve the results by constructing a compact scheme of second-order in time while keeping fourth-order in space.

Based on the L2-1σ approximation formula and a fourth-order compact finite difference approximation, the stability of the constructed scheme and its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method.

Applications using two model problems demonstrate the theoretical results.