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- Title
Numerical Finite Difference Scheme for a Two-Dimensional Time-Fractional Semilinear Diffusion Equation.
- Authors
Rasheed, Maan A.; Saeed, Maani A.
- Abstract
Time-fractional partial differential equations are foundational instruments in modeling neuronal dynamics. These equations are formulated by replacing the conventional time derivative of order α, where 0 < a < 1, in the standard equation with the Caputo fractional derivative. This study introduces the Crank-Nicolson (C.N.) finite difference scheme as a solution method for a two-dimensional, time-fractional Semilinear parabolic equation under Dirichlet boundary conditions. An in-depth investigation into the consistency, stability, and convergence of the proposed scheme is also conducted. To corroborate the theoretical findings, two numerical experiments are carried out. The scheme's efficiency, in terms of absolute errors, order of accuracy, and computational time, is meticulously evaluated and discussed. The results demonstrate that the proposed scheme, while being conditionally stable, can be utilized effectively with a high rate of convergence to compute numerical solutions for the problem at hand.
- Subjects
FINITE differences; HEAT equation; CAPUTO fractional derivatives; PARTIAL differential equations; CRANK-nicolson method
- Publication
Mathematical Modelling of Engineering Problems, 2023, Vol 10, Issue 4, p1441
- ISSN
2369-0739
- Publication type
Article
- DOI
10.18280/mmep.100440