Generalized Fourier Transform Method for Solving Nonlinear Anomalous Diffusion Equations

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 pointsource. The merit of the numerical method is that it provides a way to calculate anomalous diffusion with an arbitrary initial condition.I.

Mobile Robot Vision Image Feature Recognition Method Based on Machine Vision

“…According to the convolution characteristics of Fourier transform, it can be concluded that the transformation of each term in the summation sign in formula (7) is the product of the Fourier transforms of two functions [14].…”

Generalized Fourier transforms based on quantum uncertainty principle

“…In [10] a survey in a nutshell given on diverse known forms of Fourier analysis, including the so called short-time Fourier transforms firstly introduced by D. Gabor (1946). In [11] a generalized Fourier transform presented with the use of is the cylindrical Bessel function. We note that in known forms of Fourier analysis, the time and frequency domains commonly are not bound.…”