Numerical study for a two-dimensional time-fractional semi linear parabolic equation using linearly implicit Euler finite difference method with Caputo derivative

The time fractional equations are fundamental tools used for modeling neuronal dynamics. These equations are obtained by substituting the time derivative of order α, where 0 < α < 1, in the standard equation with the Caputo fractional formula. In this paper, the linearly implicit Euler finite...

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Bibliographic Details
Main Authors: Rasheed, Maan A., Saeed, Maani A.
Format: Conference Proceeding
Language:English
Subjects:
Boundary conditions
Convergence
Dirichlet problem
Finite difference method
Mathematical analysis
Online Access:Get full text
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Summary:The time fractional equations are fundamental tools used for modeling neuronal dynamics. These equations are obtained by substituting the time derivative of order α, where 0 < α < 1, in the standard equation with the Caputo fractional formula. In this paper, the linearly implicit Euler finite difference scheme, is employed in solving a two-dimensional time-fractional semilinear parabolic equation with Dirichlet boundary conditions. Moreover, the consistency, stability and convergence of the proposed scheme are investigated. It is proved that the proposed scheme is unconditionally stable. The theoretical findings will be supported via numerical experiments. The numerical results show that the proposed method provides an accurate strategic solution with less errors. Moreover, the numerical orders of convergence are in good agreement with the theoretical results.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0196205