Pointwise error estimate of an alternating direction implicit difference scheme for two-dimensional time-fractional diffusion equation

2021 ◽  
Vol 99 ◽  
pp. 155-161
Author(s):  
Yue Wang ◽  
Hu Chen
Keyword(s):  
Diffusion Equation ◽  
Error Estimate ◽  
Difference Scheme ◽  
Fractional Diffusion ◽  
Two Dimensional ◽  
Implicit Difference Scheme ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Pointwise Error ◽  
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.

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