Generalized Fourier transform method for nonlinear anomalous diffusion equation

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 normal diffusion equation. The feasibility of the approach is validated by comparing the numerical result with the exact solution for point-source. The merit of numerical method is that it provide a way to calculate anomalous diffusion with an arbitrary initial condition.