Numerical simulation for the two-dimensional and three-dimensional Riesz space fractional diffusion equations with delay and a nonlinear reaction term

ABSTRACT

In this research, we consider the alternating direction implicit method for solving the two-dimensional and three-dimensional Riesz space fractional diffusion equations with delay and a nonlinear reaction term. The corresponding theoretical results including stability and convergence are provided. Moreover, the convergence order of the proposed method is improved by using the Richardson extrapolation method. The numerical results are presented to show the robustness and effectiveness of the numerical method.

KEYWORDS:

• Riesz space fractional diffusion equations with delay
• nonlinear reaction term
• alternating direction method
• richardson extrapolation method
• stability and convergence

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34K37
• 35K58
• 65M06
• 65M12

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by projects from the National Natural Science Foundation of China (NSFC) under grant 11501238 and 11601180, NSF of Guangdong Province under grant 2016A030313119.