Finite Difference Approximations for Fractional Reaction-Diffusion Equations and the Application in PM2.5

DOI

10.2991/isesce-15.2015.79How to use a DOI?

Keywords

PM2.5; fractional reaction-diffusion equations; Crank-Nicolson method; numerical simulation

Abstract

In this paper, fractional reaction-diffusion equations are used to model the diffusion of PM2.5 in the air. First, based on the shifted Grünwald formula, we propose the fractional Crank-Nicolson method to solve the fractional reaction-diffusion equations. Then we prove the existence and uniqueness of numerical solutions, and establish the stability and convergence of the method. Furthermore, numerical examples are also provided to show the efficiency of the method. Finally, the diffusion of PM2.5 in Guangzhou is simulated by using this method under appropriate parameters .

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Changping Xie
AU  - Lang Li
AU  - Zhongzhan Huang
AU  - Jinyan Li
AU  - PengLiang Li
AU  - Shaomei Fang
PY  - 2015/12
DA  - 2015/12
TI  - Finite Difference Approximations for Fractional Reaction-Diffusion Equations and the Application in PM2.5
BT  - Proceedings of the 2015 International Symposium on Energy Science and Chemical Engineering
PB  - Atlantis Press
SP  - 393
EP  - 397
SN  - 2352-5401
UR  - https://doi.org/10.2991/isesce-15.2015.79
DO  - 10.2991/isesce-15.2015.79
ID  - Xie2015/12
ER  -