Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains

doi:10.1137/S0036142903421278

CSpace

	Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains
	Ma, HP ; Sun, WW ; Tang, T
	2005
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	43 期号:1 页码:58-75
摘要	Hermite spectral methods are investigated for linear diffusion equations and nonlinear convection-diffusion equations in unbounded domains. When the solution domain is unbounded, the diffusion operator no longer has a compact resolvent, which makes the Hermite spectral methods unstable. To overcome this difficulty, a time-dependent scaling factor is employed in the Hermite expansions, which yields a positive bilinear form. As a consequence, stability and spectral convergence can be established for this approach. The present method plays a similar role in the stability of the similarity transformation technique proposed by Funaro and Kavian [Math. Comp., 57 (1991), pp. 597-619]. However, since coordinate transformations are not required, the present approach is more efficient and is easier to implement. In fact, with the time-dependent scaling the resulting discretization system is of the same form as that associated with the classical (straightforward but unstable) Hermite spectral method. Numerical experiments are carried out to support the theoretical stability and convergence results.
关键词	Hermite spectral method time-dependent scaling stability convergence
DOI	10.1137/S0036142903421278
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000230502600004
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1217
专题	中国科学院数学与系统科学研究院
通讯作者	Ma, HP
作者单位	1.Shanghai Univ, Dept Math, Shanghai 200436, Peoples R China 2.City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China 3.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China 4.Chinese Acad Sci, Inst Computat Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Ma, HP,Sun, WW,Tang, T. Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2005,43(1):58-75.
APA	Ma, HP,Sun, WW,&Tang, T.(2005).Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains.SIAM JOURNAL ON NUMERICAL ANALYSIS,43(1),58-75.
MLA	Ma, HP,et al."Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains".SIAM JOURNAL ON NUMERICAL ANALYSIS 43.1(2005):58-75.