A Fourier stability study for an explicit numerical scheme applied to the fractional diffusion equation with dimensional correction
Palavras-chave:
Stability analysis, Fractional diffusion equation, Dimensional correction, Finite differences approximation, Riemann-Liouville fractional derivativesResumo
This paper presents a study of stability analysis for the generalization of the fractional diffusion equa-
tion FDE with constant coefficient, when the dimensional correction parameter τ is inserted in the model. The
numerical approach chosen is an explicit finite difference scheme inspired by the classical forward Euler method.
The fractional temporal order derivative adopted in the equation is the Riemann-Liouville one, which is approxi-
mated by the Grunwald-Letnikov operator. The stability analysis is conducted with the application of the Fourier ̈
method, allowing to show that the proposed explicit scheme is conditionally stable. A numerical experiment is
also presented with displayed results so as to back up the theoretical conclusions and to point the influence of the
dimensional correction parameter.
