Author(s)

Jie Yao^1*, Cameron L. Williams², Fazle Hussain¹, Donald J. Kouri^2,3*

¹Department of Mechanical Engineering, Texas Tech University, Lubbock, TX, USA.
²Department of Mathematics, University of Houston, Houston, TX, USA.
³Departments of Mechanical Engineering and Physics, University of Houston, Houston, TX, USA.

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.

Generalized Fourier Transform, Anomalous Diffusion, Nonlinear

Yao, J. , Williams, C. , Hussain, F. and Kouri, D. (2019) Generalized Fourier Transform Method for Solving Nonlinear Anomalous Diffusion Equations. Applied Mathematics, 10, 1039-1047. doi: 10.4236/am.2019.1012072.