Domain Decomposition Spectral Method for Mixed Inhomogeneous Boundary Value Problems of High Order Differential Equations on Unbounded Domains

In this paper, we develop domain decomposition spectral method for mixed inhomogeneous boundary value problems of high order differential equations defined on unbounded domains. We introduce an orthogonal family of new generalized Laguerre functions, with the weight function x α , α being any real n...

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Vydané v:	Journal of scientific computing Ročník 53; číslo 2; s. 451 - 480
Hlavní autori:	Zhang, Chao, Guo, Ben-yu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Boston Springer US 01.11.2012 Springer Nature B.V
Predmet:	Accuracy Algorithms Approximation Boundary conditions Boundary value problems Collocation methods Computational Mathematics and Numerical Analysis Decomposition Differential equations Domain decomposition methods Interpolation Laguerre functions Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Methods Numbers Real numbers Spectral methods Theoretical Weighting functions Laguerre-Gauss-Radau type interpolation Laguerre quasi-orthogonal approximation Domain decomposition spectral methods High order problems with mixed inhomogeneous boundary conditions
ISSN:	0885-7474, 1573-7691
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Abstract	In this paper, we develop domain decomposition spectral method for mixed inhomogeneous boundary value problems of high order differential equations defined on unbounded domains. We introduce an orthogonal family of new generalized Laguerre functions, with the weight function x α , α being any real number. The corresponding quasi-orthogonal approximation and Gauss-Radau type interpolation are investigated, which play important roles in the related spectral and collocation methods. As examples of applications, we propose the domain decomposition spectral methods for two fourth order problems, and the spectral method with essential imposition of boundary conditions. The spectral accuracy is proved. Numerical results demonstrate the effectiveness of suggested algorithms.
AbstractList	In this paper, we develop domain decomposition spectral method for mixed inhomogeneous boundary value problems of high order differential equations defined on unbounded domains. We introduce an orthogonal family of new generalized Laguerre functions, with the weight function xα, α being any real number. The corresponding quasi-orthogonal approximation and Gauss-Radau type interpolation are investigated, which play important roles in the related spectral and collocation methods. As examples of applications, we propose the domain decomposition spectral methods for two fourth order problems, and the spectral method with essential imposition of boundary conditions. The spectral accuracy is proved. Numerical results demonstrate the effectiveness of suggested algorithms. In this paper, we develop domain decomposition spectral method for mixed inhomogeneous boundary value problems of high order differential equations defined on unbounded domains. We introduce an orthogonal family of new generalized Laguerre functions, with the weight function x α , α being any real number. The corresponding quasi-orthogonal approximation and Gauss-Radau type interpolation are investigated, which play important roles in the related spectral and collocation methods. As examples of applications, we propose the domain decomposition spectral methods for two fourth order problems, and the spectral method with essential imposition of boundary conditions. The spectral accuracy is proved. Numerical results demonstrate the effectiveness of suggested algorithms.
Author	Guo, Ben-yu Zhang, Chao
Author_xml	– sequence: 1 givenname: Chao surname: Zhang fullname: Zhang, Chao organization: Jiangsu Normal University – sequence: 2 givenname: Ben-yu surname: Guo fullname: Guo, Ben-yu email: byguo@shnu.edu.cn organization: Shanghai Normal University, Scientific Computing Key Laboratory, Division of Computational Science of E-institute, Shanghai Universities
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Cites_doi	10.1090/S0025-5718-99-01059-5 10.1137/04061324X 10.1093/acprof:oso/9780198528692.001.0001 10.1090/S0025-5718-08-02152-2 10.1016/S0021-9991(02)00064-5 10.1007/PL00005413 10.1142/9789812816641 10.1016/j.jat.2008.08.016 10.1137/1.9781611970425 10.1137/S0036142999362936 10.1016/j.cam.2004.12.008 10.1016/j.apnum.2006.07.032 10.1137/070698269 10.1090/S0025-5718-03-01521-7 10.1090/S0025-5718-1991-1094949-X 10.1007/978-3-540-30726-6 10.1007/978-3-540-46783-0
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Keywords	Laguerre-Gauss-Radau type interpolation Laguerre quasi-orthogonal approximation Domain decomposition spectral methods High order problems with mixed inhomogeneous boundary conditions
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SubjectTerms	Accuracy Algorithms Approximation Boundary conditions Boundary value problems Collocation methods Computational Mathematics and Numerical Analysis Decomposition Differential equations Domain decomposition methods Interpolation Laguerre functions Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Methods Numbers Real numbers Spectral methods Theoretical Weighting functions
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Title	Domain Decomposition Spectral Method for Mixed Inhomogeneous Boundary Value Problems of High Order Differential Equations on Unbounded Domains
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