A high-order compact alternating direction implicit method for solving the 3D time-fractional diffusion equation with the Caputo–Fabrizio operator

2020 ◽  
Vol 14 (4) ◽  
pp. 359-373
Author(s):  
Narjes Abdi ◽  
Hossein Aminikhah ◽  
Amir Hossein Refahi Sheikhani ◽  
Javad Alavi
Keyword(s):  
Diffusion Equation ◽  
Fractional Diffusion ◽  
High Order ◽  
Fractional Diffusion Equation ◽  
Implicit Method ◽  
Alternating Direction Implicit Method ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Time Fractional Diffusion Equation

scholarly journals A new compact alternating direction implicit method for solving two dimensional time fractional diffusion equation with Caputo-Fabrizio derivative

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3609-3626
Author(s):  
Mehran Taghipour ◽  
Hossein Aminikhah
Keyword(s):  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Time Fractional Diffusion Equation ◽  
The Stability ◽  
Theoretical Considerations

In this paper, a new compact alternating direction implicit (ADI) difference scheme is proposed for the solution of two dimensional time fractional diffusion equation. Theoretical considerations are discussed. We show that the proposed method is fourth order accurate in space and two order accurate in time. The stability and convergence of the compact ADI method are presented by the Fourier analysis method. Numerical examples confirm the theoretical results and high accuracy of the proposed scheme.

Sign in / Sign up

Export Citation Format

Share Document