A Legendre-Petrov-Galerkin and Chebyshev collocation method for third-order differential equations

doi:10.1137/S0036142999361505

Details of Research Outputs

Status	已发表Published
Title	A Legendre-Petrov-Galerkin and Chebyshev collocation method for third-order differential equations
Creator	Ma, Heping 1; Sun, Weiwei2
Date Issued	2001
Source Publication	SIAM Journal on Numerical Analysis
ISSN	0036-1429
Volume	38 Issue:5 Pages:1425-1438
Abstract	A Legendre-Petrov-Galerkin (LPG) method for the third-order differential equation is developed. By choosing appropriate base functions, the method can be implemented efficiently. Also, this new approach enables us to derive an optimal rate of convergence in L2-norm. The method is applied to some nonlinear problems such as the Korteweg-de Vries (KdV) equation with the Chebyshev collocation treatment for the nonlinear term. It is a Legendre-Petrov-Galerkin and Chebyshev collocation (LPG-CC) method. Numerical experiments are given to confirm the theoretical result.
Keyword	Korteweg-de Vries equation Legendre-Petrov-Galerkin and Chebyshev collocation Third-order differential equation
DOI	10.1137/S0036142999361505
URL	View source
Indexed By	SCIE
Language	英语English
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied
WOS ID	WOS:000166214900002
Citation statistics	Cited Times:80[WOS] [WOS Record] [Related Records in WOS]
Document Type	Journal article
Identifier	http://repository.uic.edu.cn/handle/39GCC9TT/3298
Collection	Research outside affiliated institution
Corresponding Author	Ma, Heping
Affiliation	1.Department of Mathematics, Shanghai University, Shanghai 200436, China 2.Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
Recommended Citation GB/T 7714	Ma, Heping,Sun, Weiwei. A Legendre-Petrov-Galerkin and Chebyshev collocation method for third-order differential equations[J]. SIAM Journal on Numerical Analysis, 2001, 38(5): 1425-1438.
APA	Ma, Heping, & Sun, Weiwei. (2001). A Legendre-Petrov-Galerkin and Chebyshev collocation method for third-order differential equations. SIAM Journal on Numerical Analysis, 38(5), 1425-1438.
MLA	Ma, Heping,et al."A Legendre-Petrov-Galerkin and Chebyshev collocation method for third-order differential equations". SIAM Journal on Numerical Analysis 38.5(2001): 1425-1438.

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