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

Abstract

In this paper, a compact alternating direction implicit 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.

Keywords:

• fractional diffusion-wave equation
• finite difference scheme
• weighted and shifted Grünwald difference operator
• compact ADI scheme
• convergence

2010 AMS Subject Classifications::

• 65M06
• 65M12
• 65M15
• 35R11

Acknowledgements

The authors would like to express their gratitude to the referees for their valuable suggestions on the manuscript. This research is supported by the Macao Science and Technology Development Fund FDCT/001/2013/A and the grant MYRG086(Y2-L2)-FST12-VSW from University of Macau.