Numerical solutions and analysis of diffusion for new generalized fractional advection-diffusion equations

• Authors: Yufeng Xu , Om Agrawal
• Languages of publication: EN

Abstracts

EN

In this paper we study a class of new Generalized Fractional Advection-Diffusion Equations (GFADEs) with a new Generalized Fractional Derivative (GFD) proposed last year. The new GFD is defined in the Caputo sense using a weight function and a scale function. The GFADE is discussed in a bounded domain, and numerical solutions for two examples consisting of a linear and a nonlinear GFADE are obtained using an implicit finite difference approach. The stability of the numerical scheme is investigated, and the order of convergence is estimated numerically. Numerical results illustrate that the finite difference scheme is simple and effective for solving the GFADEs. We investigate the influence of weight and scale functions on the diffusion of GFADEs. Linear and nonlinear stretching and contracting functions are considered. It is found that an increasing weight function increases the rate of diffusion, and a scale function can stretch or contract the diffusion on the time domain.

Keywords

EN

generalized fractional derivative; finite difference method; advection-diffusion equations; convergence; stability

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 10
• Pages: 1178-1193

Dates

published

1 - 10 - 2013

online

19 - 12 - 2013

Contributors

author

Yufeng Xu

• Department of Applied Mathematics, School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

author

Om Agrawal

• Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, Illinois, 62901, USA

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Identifiers

DOI

10.2478/s11534-013-0295-0