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

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.