**Volume 11, Issue 1, pp 17--25**

**Publication Date**: 2017-12-22

http://dx.doi.org/10.22436/jnsa.011.01.03

Shuiping Yang - School of Mathematics and Big Data Science, Huizhou University, Guangdong, 516007, China

In this paper, we propose a finite difference method for the Riesz space fractional diffusion equations with delay and a nonlinear source term on a finite domain. The proposed method combines a time scheme based on the predictor-corrector method and the Crank-Nicolson scheme for the spatial discretization. The corresponding theoretical results including stability and convergence are provided. Some numerical examples are presented to validate the proposed method.

Riesz fractional derivative, fractional diffusion equations, Crank-Nicolson scheme, stability, convergence

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