A compact ADI Crank–Nicolson difference scheme for the two-dimensional time fractional subdiffusion equation

ABSTRACT

In this paper, a compact alternating direction implicit (ADI) Crank–Nicolson difference scheme is proposed and analysed for the solution of two-dimensional time fractional subdiffusion equation. The Riemann–Liouville time fractional derivative is approximated by the weighted and shifted Grünwald difference operator and the spatial derivative is discretized by a fourth-order compact finite difference method. The stability and convergence of the difference scheme are discussed and theoretically proven by using the energy method. Finally, numerical experiments are carried out to show that the numerical results are in good agreement with the theoretical analysis.

KEYWORDS:

• Compact ADI scheme
• Crank–Nicolson difference scheme
• fractional subdiffusion equation
• convergence
• stability

2010 AMS SUBJECT CLASSIFICATIONS:

• 65M06
• 65M12
• 65M15

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was partially supported by the National Natural Science Foundation of China under [grant number 11501150 and 11271101]; the Key Project of Science and Technology of Weihai [grant number 2014DXGJ14]; the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology [grant number 2016081]; the Disciplinary Construction Guide Foundation of Harbin Institute of Technology at Weihai [grant number 20140206]; the Scientific Research Foundation of Harbin Institute of Technology at Weihai [grant number 201319].