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 $O\left({\tau }^{3-\alpha }\right)$, $1<\alpha <2$ and the space derivatives are discretized with a sixth-order compact procedure. The solvability, stability and $H^1$ 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.