TITLE:
Generalized Fourier Transform Method for Solving Nonlinear Anomalous Diffusion Equations
AUTHORS:
Jie Yao, Cameron L. Williams, Fazle Hussain, Donald J. Kouri
KEYWORDS:
Generalized Fourier Transform, Anomalous Diffusion, Nonlinear
JOURNAL NAME:
Applied Mathematics,
Vol.10 No.12,
December
23,
2019
ABSTRACT: The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion function. The generalized Fourier transform approach is the extension of the Fourier transform method used for the normal diffusion equation. The feasibility of the approach is validated by comparing the numerical result with the exact solution for a point-source. The merit of the numerical method is that it provides a way to calculate anomalous diffusion with an arbitrary initial condition.