A note on compact finite difference method for reaction-diffusion equations with delay

Dongfang Li; Chengjian Zhang; Jinming Wen

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A note on compact finite difference method for reaction-diffusion equations with delay

机译：带时滞反应扩散方程的紧致差分法的注记

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摘要

In this short study, we investigate the long time stability of the compact finite difference method for the reaction-diffusion equations with delay. It is shown that the spatial discretization leads to a reduction of the asymptotic stability region of the corresponding PDE if the compact finite difference method is applied to discretize the diffusion operator. A way to improve the stability region of the method is also presented. Finally, some numerical experiments are proposed to confirm our findings.

机译：在这项简短的研究中，我们研究了时滞反应扩散方程的紧凑有限差分方法的长期稳定性。结果表明，如果采用紧凑有限差分法离散化扩散算子，则空间离散化会导致相应PDE渐近稳定区域的减小。还提出了一种改善方法稳定性区域的方法。最后，提出了一些数值实验来证实我们的发现。

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来源
《Applied Mathematical Modelling》 |2015年第6期|1749-1754|共6页
作者
Dongfang Li; Chengjian Zhang; Jinming Wen;
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作者单位

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China,Department of Mathematics and Statistics, McGill Uninversity, Montreal, Quebec H3A2K6, Canada;

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;

Department of Mathematics and Statistics, McGill Uninversity, Montreal, Quebec H3A2K6, Canada;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Long time stability; Preserve stability; Compact finite difference method; Reaction-diffusion equations with delay;

机译：长时间稳定;保持稳定性;紧凑有限差分法;时滞反应扩散方程;

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1. Convergence and stability of compact finite difference method for nonlinear time fractional reaction-diffusion equations with delay [J] . Li Lili, Zhou Boya, Chen Xiaoli, Applied mathematics and computation . 2018,第期

机译：具有延迟的非线性时间分数反应扩散方程的紧凑有限差分方法的收敛性和稳定性
2. HIGHER-ORDER LINEARIZED MULTISTEP FINITE DIFFERENCE METHODS FOR NON-FICKIAN DELAY REACTION-DIFFUSION EQUATIONS [J] . Zhang Qifeng, Mei Ming, Zhang Chengjian International journal of numerical analysis and modeling . 2017,第1期

机译：非Fickian延迟反应扩散方程的高阶线性化多步有限差分方法
3. Higher-order compact finite difference method for systems of reaction-diffusion equations [J] . Wang YM, Zhang HB Journal of Computational and Applied Mathematics . 2009,第2期

机译：反应扩散方程组的高阶紧致差分法
4. A comparative study of compact finite volume methods for the 3-D diffusion equations with finite difference ADI and SOR [C] . Borah, B.N., White, . 1993

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5. Finite difference delay modeling for time domain integral equations of electromagnetics. [D] . Wang, Xiaobo. 2010

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6. A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction-Diffusion Equations on Surfaces [O] . Varun Shankar, Grady B. Wright, Robert M. Kirby, -1

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7. A Radial Basis Function (RBF) Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces [O] . Lehto, Erik, Shankar, Varun, Wright, Grady B. 2017

机译：表面反应扩散方程的径向基函数（RBF）紧凑有限差分（FD）方案

A note on compact finite difference method for reaction-diffusion equations with delay

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