Efficient second-order ADI difference schemes for three-dimensional Riesz space-fractional diffusion equations

2021 ◽  
Vol 98 ◽  
pp. 24-39
Author(s):  
Chen Zhu ◽  
Bingyin Zhang ◽  
Hongfei Fu ◽  
Jun Liu
Keyword(s):  
Three Dimensional ◽  
Fractional Diffusion ◽  
Second Order ◽  
Riesz Space ◽  
Difference Schemes ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations

scholarly journals Fractional Diffusion Equations for Lattice and Continuum: Grünwald-Letnikov Differences and Derivatives Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Fractional Derivatives ◽  
Three Dimensional ◽  
Lattice Models ◽  
Fractional Diffusion ◽  
Lattice Diffusion ◽  
Diffusion Equations ◽  
Difference Operators ◽  
Fractional Diffusion Equations ◽  
Nonlocal Media ◽  
Derivatives Of

Fractional diffusion equations for three-dimensional lattice models based on fractional-order differences of the Grünwald-Letnikov type are suggested. These lattice fractional diffusion equations contain difference operators that describe long-range jumps from one lattice site to another. In continuum limit, the suggested lattice diffusion equations with noninteger order differences give the diffusion equations with the Grünwald-Letnikov fractional derivatives for continuum. We propose a consistent derivation of the fractional diffusion equation with the fractional derivatives of Grünwald-Letnikov type. The suggested lattice diffusion equations can be considered as a new microstructural basis of space-fractional diffusion in nonlocal media.

Sign in / Sign up

Export Citation Format

Share Document