带周期边界复Ginzburg-Landau方程的四阶显格式  

FOURTH ORDER EXPLICIT SCHEME FOR COMPLEX GINZBURG-LANDAU EQUATION WITH PERIODIC BOUNDARY CONDITION

作　　者：张启峰 熊海洋[2] 徐定华 徐映红[2] Zhang Qifeng;Xiong Haiyang;Xu Dinghua;Xu Yinghong(School of Mathematics,Southeast University,Nanjing 201096/ Department of Mathematics,School of Science,Zhejiang Sci-Tech University, Hangzhou 310018;Department of Mathematics,School of Science,Zhejiang Sci-Tech University, Hangzhou 310018)

机构地区：[1]东南大学数学系,南京210096 [2]浙江理工大学理学院数学系,杭州310018

出　　处：《高等学校计算数学学报》2018年第4期313-330,共18页Numerical Mathematics A Journal of Chinese Universities

基　　金：浙江省自然科学基金(LY19A010026);中国博士后科学基金资助项目(2018M642131);国家自然科学基金(11501514;11871435;11501513)

摘　　要：1引言复Ginzburg-Landau方程在化学、生物学和物理学的许多分支,如超导性、超流性、非线性光学和Bose-Einstein凝聚等问题上被广泛研究[1,2].然而,只有极少数的Ginzburg-Landau方程能在理论上得到精确的解析解.因此,在实际应用中,寻求一个具有较高的数值精度、较好的稳定性与收敛性的数值解法不仅有重要的理论意义,也有重要的实用价值.The complex Ginzburg-Landau equation is often encountered in physics and engineering applications.However,it remains,a challenge to develop a simple,stable and accurate finite difference scheme for solving this equation due to the nonlinear term.In this paper,we study a three level linearized fourth-order accurate numerical method for the Ginzburg-Landau equation with periodic boundary condition.Firstly,we construct a class of three level linearized finite difference method for the Ginzburg-Landau equation with periodic boundary condition.Secondly,we analyze the uniqueness and convergence of the numerical method,and prove that the convergence order of the numerical method is О(Г^2+h^4).Finally, we verify the accuracy and validity of the numerical method by two numerical examples.

关 键 词：复GINZBURG-LANDAU方程 BOSE-EINSTEIN凝聚 周期边界 显格式 四阶 非线性光学 数值精度 数值解法 

分 类 号：O241.82[理学—计算数学]