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	On the time splitting spectral method for the complex Ginzburg-Landau equation in the large time and space scale limit
	Degond, P. ; Shi Jin ; Min Tang
	2010-10-12 ; 2010-10-12
关键词	Theoretical or Mathematical/ Ginzburg-Landau theory nonlinear equations Schrodinger equation/ time splitting spectral method complex Ginzburg-Landau equation space scale limit numerical approximation nonlinear Schrodinger limit asymptotic preserving/ A0230 Function theory, analysis A0547 Nonlinear dynamical systems and bifurcations A0365G Solutions of wave equations: bound state in quantum theory B0290K Nonlinear and functional equations (numerical analysis) C4150 Nonlinear and functional equations (numerical analysis)
中文摘要	We are interested in the numerical approximation of the complex Ginzburg-Landau equation in the large time and space limit. There are two interesting regimes in this problem, one being the large space time limit, and one being the nonlinear Schrodinger limit. These limits have been studied analytically in, for example, T. Colin and A. Soyeur, Asymptot. Anal., 13 (1996), pp. 361-372; F. H. Lin, Comm. Pure Appl. Math., 51 (1998), pp. 385-441; F. H. Lin and J. X. Xin, Comm. Math. Phys., 200 (1999), pp. 249-274. We study a time splitting spectral method for this problem. In particular, we are interested in whether such a scheme is asymptotic preserving (AP) with respect to these two limits. Our results show that the scheme is AP for the first limit but not the second one. For the large space time limit, our numerical experiments show that the scheme can capture the correct physical behavior without resolving the small scale dynamics, even for transitional problems, where small and large scales coexist.
语种	英语
出版者	Society for Industrial and Applied Mathematics ; USA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/81323]
专题	清华大学
推荐引用方式 GB/T 7714	Degond, P.,Shi Jin,Min Tang. On the time splitting spectral method for the complex Ginzburg-Landau equation in the large time and space scale limit[J],2010, 2010.
APA	Degond, P.,Shi Jin,&Min Tang.(2010).On the time splitting spectral method for the complex Ginzburg-Landau equation in the large time and space scale limit..
MLA	Degond, P.,et al."On the time splitting spectral method for the complex Ginzburg-Landau equation in the large time and space scale limit".(2010).

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