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