Generalized Fourier transform method for nonlinear anomalous diffusion equation

Jie Yao; Cameron L. Williams; Fazle Hussain; Donald J. Kouri

Generalized Fourier transform method for nonlinear anomalous diffusion equation

Jie Yao, Cameron L. Williams, Fazle Hussain, Donald J. Kouri

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	Unknown Journal
State	Published - Jan 12 2017

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title = "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 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.",

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year = "2017",

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AU - Yao, Jie

AU - Williams, Cameron L.

AU - Hussain, Fazle

AU - Kouri, Donald J.

PY - 2017/1/12

Y1 - 2017/1/12

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:85093761041

JO - Unknown Journal

JF - Unknown Journal

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