Mathematical Methods in the Applied Sciences

Volume 38, Issue 15 pp. 3308-3321

Research Article

A non-standard finite difference scheme for an advection-diffusion-reaction equation

Wendi Qin,

Wendi Qin

Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China

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Deqiong Ding,

Corresponding Author

Deqiong Ding

Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China

Correspondence to: Deqiong Ding, Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China.

E-mail: [email protected], [email protected]

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Xiaohua Ding,

Xiaohua Ding

Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China

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Wendi Qin,

Wendi Qin

Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China

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Deqiong Ding,

Corresponding Author

Deqiong Ding

Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China

Correspondence to: Deqiong Ding, Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China.

E-mail: [email protected], [email protected]

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Xiaohua Ding,

Xiaohua Ding

Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China

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First published: 01 October 2014

https://doi.org/10.1002/mma.3297

Citations: 3

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Abstract

In this note, a non-standard finite difference (NSFD) scheme is proposed for an advection-diffusion-reaction equation with nonlinear reaction term. We first study the diffusion-free case of this equation, that is, an advection-reaction equation. Two exact finite difference schemes are constructed for the advection-reaction equation by the method of characteristics. As these exact schemes are complicated and are not convenient to use, an NSFD scheme is derived from the exact scheme. Then, the NSFD scheme for the advection-reaction equation is combined with a finite difference space-approximation of the diffusion term to provide a NSFD scheme for the advection-diffusion-reaction equation. This new scheme could preserve the fixed points, the positivity, and the boundedness of the solution of the original equation. Numerical experiments verify the validity of our analytical results. Copyright © 2014 JohnWiley & Sons, Ltd.

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Volume38, Issue15

October 2015

Pages 3308-3321

A non-standard finite difference scheme for an advection-diffusion-reaction equation

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A non-standard finite difference scheme for an advection-diffusion-reaction equation

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