A new implicit compact difference scheme for the fourth-order fractional diffusion-wave system

Abstract

In this paper, a new implicit compact difference scheme is constructed for the fourth-order fractional diffusion-wave system by the method of order reduction. The temporal Caputo fractional derivative is discretized by an L₁ scheme. The spatial derivative of order 4 is reduced to one of order 2 by order reduction. Then, the reduced derivative of order 2 is discretized by a difference formula of order 4. Using order reduction, two simple and accurate formulae of discretization for the derivative boundary conditions are obtained. And a new way of proving the stability and convergence of the scheme is presented in this paper. Some numerical results demonstrate the accuracy and efficiency of our new scheme.

Keywords:

• diffusion-wave system
• method of order reduction
• implicit compact difference scheme
• stability
• convergence

2010 AMS Subject Classifications:

• 65M06
• 65M12

Acknowledgements

This work is partially supported by the National Science Foundation of China under grant 11102179, Jiangsu Province Science Foundation under grant SBK201220691 and PAPD of Jiangsu Higher Education Institutions.