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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.
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.