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Generalized Fourier Transform Method for Solving Nonlinear Anomalous Diffusion Equations
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX, USA
Department of Mathematics, University of Houston, Houston, TX, USA
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX, USA
Departments of Mechanical Engineering and Physics, University of Houston, Houston, TX, USA
- 1 Department of Mechanical Engineering, Texas Tech University, Lubbock, TX, USA
- 2 Department of Mathematics, University of Houston, Houston, TX, USA
- 3 Department of Mechanical Engineering, Texas Tech University, Lubbock, TX, USA
- 4 Departments of Mechanical Engineering and Physics, University of Houston, Houston, TX, USA
Applied Mathematics·Volume 10 (2019)·Pages 1039–1047·Published 10 December 2019·DOI10.4236/am.2019.1012072
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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.
KeywordsGeneralized Fourier TransformAnomalous DiffusionNonlinear
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