Second-order BDF time approximation for Riesz space-fractional diffusion equations

ABSTRACT

Second-order backward difference formula (BDF2) is considered for time approximation of Riesz space-fractional diffusion equations. The Riesz space derivative is approximated by the second-order fractional centre difference formula. To improve the computational efficiency, an alternating directional implicit scheme is also proposed for solving two-dimensional space-fractional diffusion problems. Numerical experiments are provided to verify our theory and to show the effectiveness of numerical algorithms.

Keywords:

• Fractional diffusion equation
• Riesz space derivative
• fractional centred difference
• BDF2 formula
• discrete energy method

2010 AMS subject classifications:

• 65M06
• 65M12
• 65M15

Acknowledgements

The authors would like to thank the editor and referees for their helpful comments which have improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was partially supported by the research grant numbers MYRG2015-00064-FST and MYRG2017-00098-FST from Universidade de Macau, the grant numbers 11001271 and 11372354 from National Science Foundation of China and the grant numbers BRA2015518 from 333 High-level Personal Training Project of Jiangsu Province.