A fourth-order compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equation

Abstract

In this paper, a second-order backward difference formula (abbr. BDF2) is used to approximate first-order time partial derivative, the Riesz fractional derivatives are approximated by fourth-order compact operators, a class of new alternating-direction implicit difference scheme (abbr. ADI) is constructed for two-dimensional Riesz space fractional nonlinear reaction–diffusion equation. Stability and convergence of the numerical method are analysed. Numerical experiments demonstrate that the proposed method is effective.

Keywords:

• Riesz space fractional derivative
• BDF2 formula
• fourth-order compact operator
• ADI scheme
• stability
• convergence

2010 Mathematics Subject Classifications:

• 26A33
• 65M06
• 65M12

Acknowledgments

The authors would like to express the thanks to the referees for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Science Foundation of China [grant number 11671343], and Project of Scientific Research Fund of Hunan Provincial Science and Technology Department [grant number 2018WK4006].