A high order ADI scheme for the two-dimensional time fractional diffusion-wave equation

TL;DR

This paper introduces a high-order ADI finite difference scheme for 2D time fractional diffusion-wave equations, achieving second-order temporal and fourth-order spatial accuracy, surpassing previous methods.

Contribution

The paper develops a compact ADI scheme that attains second-order accuracy in time for the first time in this context.

Findings

Achieves second-order temporal accuracy in 2D fractional diffusion-wave equations.

Provides a fourth-order spatial accuracy scheme.

Demonstrates improved numerical stability and efficiency.

Abstract

In this paper, a compact alternating direction implicit (ADI) finite difference scheme for the two-dimensional time fractional diffusion-wave equation is developed, with temporal and spatial accuracy order equal to two and four respectively. The second order accuracy in the time direction has not been achieved in previous studies.