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.
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).