Investigations on several compact ADI methods for the 2D time fractional diffusion equation

ABSTRACT

In this article, based on the superconvergent approximation for fractional derivative and the Riemann-Liouville fractional integral, several compact alternating direction implicit (ADI) methods are investigated for solving the 2D time fractional diffusion equation with subdiffusion α ∈ (0, 1). All these methods are second-order-accurate in time and fourth-order-accurate in space, which are independent of the values of anomalous diffusion exponent α. The unconditional stability of the first two methods is discussed by the Fourier analysis method. Numerical examples are computed to justify the theoretical results, and comparisons are made among these methods.

Acknowledgments

The authors would like to thank the editor and referees for their valuable comments and suggestions which helped us to improve the results of this article. The authors also thank Dr. Dongwei Gui (Cele National Station of Observation & Research for Desert-Grassland Ecosystem in Xinjiang) for his support and encouragement in this work.