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Original Articles

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

Pages 1957-1978 | Received 26 Feb 2018, Accepted 29 Oct 2018, Published online: 13 Nov 2018
 

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.

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

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.

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