复Ginzburg-Landau方程的数值模拟  

Numerical Methods for the Complex Ginzburg-Landau Equation

作　　者：裴琴娟[1] 杨忍军[2] 许秋滨[2] 

机构地区：[1]常州纺织服装职业技术学院,常州213164 [2]南京审计学院数学与统计学院,南京211815

出　　处：《工程数学学报》2010年第4期693-698,共6页Chinese Journal of Engineering Mathematics

摘　　要：本文对复Ginzburg-Landau方程的周期边界问题构造了三个数值格式。其中两个差分格式的精度分别为O(τ2+h2),谱方法的精度为O(τ2+hm),其中m为方程的光滑度。用线性化分析的方法给出了格式的稳定性条件,并给出了数值实验。数值实验表明,四阶紧致格式的计算效果最好,既能达到较高的计算精度又能节省大量的计算时间。In this paper, three numerical schemes are studied for the complex Ginzburg-Landau equation with periodic boundary conditions. The truncation error of the two di？erence schemes are O（τ^2＋h^4）. The truncation error of the spectral method is O（τ^2＋h^m）, where m denotes the smoothness of the differential equation. The stability of three schemes is analyzed by a linear method, and numerical experiments denote that our schemes are effective and reliable. The computing results demonstrate that the fourth order compact scheme is the best, which can reach a high accuracy with shorter computing time.

关 键 词：GINZBURG-LANDAU方程 紧致差分格式 谱方法 稳定性 

分 类 号：O241.82[理学—计算数学]