Chebyshev谱配置方法求解反应扩散方程组  

AN EFFICIENT CHEBYSHEV SPECTRAL COLLOCATION METHOD FOR THE SOLUTION OF REACTION DIFFUSION SYSTEMS

作　　者：张荣培 李明军[2] 蔚喜军[3] 

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034 [2]湘潭大学数学与计算科学学院,湘潭411105 [3]北京应用物理与计算数学研究所计算物理实验室,北京100088

出　　处：《数值计算与计算机应用》2017年第4期271-281,共11页Journal on Numerical Methods and Computer Applications

基　　金：国防科技重点实验室基金(6142A050202);国家自然科学基金(11571002;11171281;61703290);中国工程物理研究院科学基金(2013A0202011;201580101021);国防基础科研计划资助(B1520133015)

摘　　要：本文讨论了一种求解二维反应扩散方程组的高精度谱配置方法.考虑边界条件为齐次Neumann边界,在空间上采用Chebyshev谱配置方法离散,得到非线性常微分方程组(ODEs).在时间方向上,采用紧致隐式积分因子方法求解.该方法结合了谱方法和紧致隐式积分因子方法的特点,具有精度高,稳定性好,存储量小以及计算时间快等优点.最后给出数值算例验证了该方法的有效性.This paper discusses a new highly accurate spectral collocation method for the two- dimensional nonlinear reaction diffusion equations with Neumann boundary condition. Inthis work, first we apply the Chebyshev spectral collocation method for the space discretiza- tion of the reaction diffusion systems. We develop a nonlinear ordinary differential equations （ODEs） in matrix formulation after space discretization. The compact implicit integration factor （cIIF） method is later applied for the nonlinear ODEs. In this approach, the storage and CPU cost are significantly reduced such that the use of cIIF method becomes attrac- tive for two-dimensional reaction diffusion equations. Numerical results are presented to demonstrate the accuracy, stability, and efficiency of the method.

关 键 词：Chebyshev谱配置 非线性 反应扩散方程组 紧致隐积分因子 

分 类 号：O241.8[理学—计算数学]