Finite difference schemes for the two-dimensional multi-term time-fractional diffusion equations with variable coefficients

2021 ◽  
Vol 40 (5) ◽  
Author(s):  
Mingrong Cui
Keyword(s):  
Finite Difference ◽  
Fractional Diffusion ◽  
Variable Coefficients ◽  
Difference Schemes ◽  
Diffusion Equations ◽  
Finite Difference Schemes ◽  
Two Dimensional ◽  
Fractional Diffusion Equations

Finite difference scheme for the time-space fractional diffusion equations

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Jianxiong Cao ◽  
Changpin Li
Keyword(s):  
Finite Difference ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Stability And Convergence ◽  
Finite Difference Schemes ◽  
Order Accuracy ◽  
Fractional Diffusion Equations ◽  
Time Space ◽  
Liouville Fractional Derivative ◽  
The Stability

AbstractIn this paper, we derive two novel finite difference schemes for two types of time-space fractional diffusion equations by adopting weighted and shifted Grünwald operator, which is used to approximate the Riemann-Liouville fractional derivative to the second order accuracy. The stability and convergence of the schemes are analyzed via mathematical induction. Moreover, the illustrative numerical examples are carried out to verify the accuracy and effectiveness of the schemes.

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