Brusselator模型的空间谱插值配点方法数值模拟
Numerical Simulation of the Brusselator Model with Spatial Spectral Interpolation Coordination Method
摘要: 该文研究一类非线性反应扩散方程组Brusselator模型，因此寻找一种简单有效的非线性反应扩散系统的数值方法是非常重要的。基于这一问题，本文提出了采用这种新的空间谱插值配点方法模拟了一些数值算例，其结果和理论上的吻合较好，结果表明了该方法的有效性。
Abstract: This paper studies the Brusselator model of a class of nonlinear reaction-diffusion equations, so it is very important to find a simple and effective numerical method for nonlinear reaction-diffusion systems. Based on this problem, some numerical examples are simulated by using this new spatial spectral interpolation collocation method.
文章引用：班亭亭, 王玉兰. Brusselator模型的空间谱插值配点方法数值模拟[J]. 应用数学进展, 2020, 9(5): 708-721. https://doi.org/10.12677/AAM.2020.95084

参考文献

[1] Kang, H. and Pesin, Y. (2005) Dynamics of a Discrete Brusselator Model: Escape to Infinity and Julia Set. Milan Journal of Mathematics, 73, 1-17. [Google Scholar] [CrossRef] 
[2] Mittal, R.C. and Jiwari, R. (2011) Numerical Solution of Two-Dimensional Reaction-C Diffusion Brusselator System. Applied Mathematics & Computation, 217, 5404-5415. [Google Scholar] [CrossRef] 
[3] Tyson, J.J. (1976) The Belousov-Zhabotinskii Reaction. In: Lecture Notes in Biomathematics 10, Springer-Verlag, Heidelberg. [Google Scholar] [CrossRef] 
[4] Wang, Y.M. and Zhang, H.B. (2009) Higher-Order Compact Finite Difference Method for Systems of Reaction Diffusion Equations. Journal of Computational and Applied Mathematics, 233, 502-518. [Google Scholar] [CrossRef] 
[5] Macha, J., Benes, M. and Strachota, P. (2017) Nonlinear Galerkin Finite Element Method Applied to the System of Reaction-C Diffusion Equations in One Space Dimension. Computers and Mathematics with Applications, 73, 2053- 2065. [Google Scholar] [CrossRef] 
[6] Harizanov, S., Lazarov, R., Margenov, S., et al. (2019) Numerical Solution of Fractional Diffusion Creaction Problems Based on BURA. Computers and Mathematics with Applications. [Google Scholar] [CrossRef] 
[7] 唐晓栋. 多反馈反应扩散系统斑图动力学研究[D]: [博士学位论文]. 徐州: 中国矿业大学, 2014.
[8] Siraj-ul-Islam, A.A. and Haq, S. (2010) A Computational Modeling of the Behavior of the Two-Dimensional Reaction-Diffusion Brusselator System. Applied Mathematical Modelling, 34, 3896-3909. [Google Scholar] [CrossRef] 
[9] Zhang, X. (2015) Efficient Solution of Differential Equation Based on MATLAB: Spectral Method Principle and Implementation. Mechanical Industry Press, Beijing.
[10] 李庆阳, 王能超, 易大义. 数值分析[M]. 第5版. 北京: 清华大学出版社, 2008.
[11] Peng, Y.H. and Ling, H. (2018) Pattern formation in a Ratio-Dependent Predator-Prey Model with Cross-Diffusion. Applied Mathematics and Computation, 331, 307-318. [Google Scholar] [CrossRef] 
[12] 熊晓华, 周天寿. Brusselator模型的定性分析及数值模拟[J]. 江西师范大学学报(自然科学版), 2007, 31(2): 164-168.
[13] Guckenheimer, J. and Holmes, P. (1999) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, New York.
[14] Sey del, R. (1999) Practical Bifurcation and Stability Analysis. From Equilibrium to Chaos, Second Edition, Springer-Verlag, New York.
[15] 周天寿. 线性耦合振子中的回声波及其稳定性[J]. 江西师范大学学报: 自然科学版, 2006, 30(1): 1-6.

为你推荐