Effect of the nodes near boundary points on the stability analysis of sixth-order compact finite difference ADI scheme for the two-dimensional time fractional diffusion-wave equation

Abstract

In this paper, the aim is to present a high-order compact alternating direction implicit (ADI) scheme for the two-dimensional time fractional diffusion-wave (FDW) equation. The time fractional derivative which has been described in the Caputo’s sense is approximated by a scheme of order O(τ3−α), 1<α<2 and the space derivatives are discretized with a sixth-order compact procedure. The solvability, stability and H1 norm of the scheme are proved. Numerical results are provided to verify the accuracy and efficiency of the proposed method of solution. The sixth-order accuracy in the space directions has not been achieved in previously studied schemes.