An alternating direction implicit fractional trapezoidal rule type difference scheme for the two-dimensional fractional evolution equation

Abstract

An alternating direction implicit (ADI) fractional trapezoidal rule (FTR) type difference scheme is formulated and analysed for a two-dimensional fractional evolution equation. In this method, standard central difference approximation used for the spatial discretization and the time stepping – an ADI scheme based on FTR, combined with chosen second-order fractional quadrature rule suggested by Lubich, are considered. The L², H¹-stability and convergence are derived. Numerical experiments in total agreement with our analysis are reported.

Keywords:

• two-dimensional fractional evolution equation
• alternating direction implicit method
• fractional trapezoidal rule type difference scheme
• stability
• convergence
• numerical experiments

2010 AMS Subject Classifications:

• 65M60
• 45K05
• 65D32

Acknowledgements

I am grateful to Professor Siqing Gan, Zhizhong Sun and the referees for many helpful suggestions. The project supported by the National Natural Science Foundation of China (No. 10971062) and the Scientific Research Foundation of Central South University of Forestry and Technology (QJ2011001A).