scholarly journals Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay

2022 ◽  
Vol 14 (1) ◽  
pp. 56-78
Author(s):  
global sci
Keyword(s):  
Time Delay ◽  
Numerical Methods ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations

scholarly journals Second-order numerical methods for the tempered fractional diffusion equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zeshan Qiu ◽  
Xuenian Cao
Keyword(s):  
Numerical Methods ◽  
Numerical Experiments ◽  
Fractional Derivatives ◽  
Fractional Diffusion ◽  
Second Order ◽  
Diffusion Equations ◽  
Difference Operators ◽  
Numerical Schemes ◽  
Fractional Diffusion Equations ◽  
Left And Right

AbstractIn this paper, a class of second-order tempered difference operators for the left and right Riemann–Liouville tempered fractional derivatives is constructed. And a class of second-order numerical methods is presented for solving the space tempered fractional diffusion equations, where the space tempered fractional derivatives are evaluated by the proposed tempered difference operators, and in the time direction is discreted by the Crank–Nicolson method. Numerical schemes are proved to be unconditionally stable and convergent with order $O(h^{2}+\tau ^{2})$O(h2+τ2). Numerical experiments demonstrate the effectiveness of the numerical schemes.

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