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.
Share and Cite
ISRP Style
Shuiping Yang, Finite difference method for Riesz space fractional diffusion equations with delay and a nonlinear source term, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 1, 17--25
AMA Style
Yang Shuiping, Finite difference method for Riesz space fractional diffusion equations with delay and a nonlinear source term. J. Nonlinear Sci. Appl. (2018); 11(1):17--25
Chicago/Turabian Style
Yang, Shuiping. "Finite difference method for Riesz space fractional diffusion equations with delay and a nonlinear source term." Journal of Nonlinear Sciences and Applications, 11, no. 1 (2018): 17--25
Keywords
- Riesz fractional derivative
- fractional diffusion equations
- Crank-Nicolson scheme
- stability
- convergence
MSC
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