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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Bibliographic Details
Published in:Journal of scientific computing Vol. 53; no. 2; pp. 451 - 480
Main Authors: Zhang, Chao, Guo, Ben-yu
Format: Journal Article
Language:English
Published: Boston Springer US 01.11.2012
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-012-9581-z