Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation

2012 ◽  
Vol 62 (3) ◽  
pp. 383-409 ◽  
Author(s):  
Mingrong Cui
Keyword(s):  
Diffusion Equation ◽  
Convergence Analysis ◽  
Fractional Diffusion ◽  
High Order ◽  
Fractional Diffusion Equation ◽  
Two Dimensional ◽  
Alternating Direction Implicit ◽  
Implicit Schemes ◽  
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.

scholarly journals An inverse source problem for a two dimensional time fractional diffusion equation with involution

2021 ◽  
Author(s):  
Batirkhan Turmetov ◽  
B. J. Kadirkulov
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Diffusion Equation ◽  
Fourier Method ◽  
Dirichlet Condition ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Inverse Source Problem ◽  
Two Dimensional ◽  
Time Fractional Diffusion Equation

In this paper, we consider a two-dimensional generalization of the parabolic equation. Using the Fourier method, we study the solvability of the inverse problem with the Dirichlet condition and periodic conditions.

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