Finite difference method for Riesz space fractional diffusion equations with delay and a nonlinear source term

Volume 11, Issue 1, pp 17--25 http://dx.doi.org/10.22436/jnsa.011.01.03

Publication Date: December 22, 2017 Submission Date: August 02, 2017 Revision Date: November 03, 2017 Accteptance Date: December 01, 2017

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Authors

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

Abstract

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.

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Keywords

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

MSC

•  34K28
•  65M12
•  35R11
•  34K37

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