Top

Journal of Scientific Computing

Published in:

01-11-2012

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

Authors: Chao Zhang, Ben-yu Guo

Published in: Journal of Scientific Computing | Issue 2/2012

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

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.

previous article A Fast Preconditioned Iterative Algorithm for the Electromagnetic Scattering from a Large Cavity

next article Erratum to: Method of Moving Frames to Solve Conservation Laws on Curved Surfaces

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Auteri, F., Parolini, N., Quartapelle, L.: Essential imposition of Neumann condition in Galerkin-Legendre elliptic solver. J. Comput. Phys. 185, 427–444 (2003) MathSciNetMATHCrossRef

Azaiez, M., Shen, J., Xu, C., Zhuang, Q.: A Laguerre-Legendre spectral method for the Stokes problems in a semi-infinite channel. SIAM J. Numer. Anal. 47, 271–292 (2008) MathSciNetCrossRef

Bernardi, C., Maday, Y.: Spectral methods. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis. Techniques of Scientific Computing, vol. 5 pp. 209–486. Amsterdam, Elsevier (1997)

Bernardi, C., Coppoletta, G., Maday, Y.: Some spectral approximations of multi-dimensional fourth-order problems. Internal report 90021, Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, Paris (1990)

Boyd, J.P.: Chebyshev and Fourier Spectral Methods, 2nd edn. Dover, New York (2001) MATH

Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods, Fundamentals in Single Domains. Springer, Berlin (2006) MATH

Funaro, D.: Polynomial Approximations of Differential Equations. Springer, Berlin (1992)

Funaro, D., Kavian, O.: Approximation of some diffusion evolution equations in unbounded domains by Hermite function. Math. Comput. 57, 597–619 (1999) MathSciNet

Gottlieb, D., Orszag, S.A.: Numerical Analysis of Spectral Methods: Theory and Applications. SIAM/CBMS, Philadelphia (1977) MATHCrossRef

10.

Guo, B.-y.: Spectral Methods and Their Applications. World Scientific, Singapore (1998) MATHCrossRef

11.

Guo, B.-y.: Error estimation of Hermite spectral method for nonlinear partial differential equations. Math. Comput. 68, 1067–1078 (1999) MATHCrossRef

12.

Guo, B.-y., Ma, H.-p.: Composite Legendre-Laguerre approximation in unbounded domains. J. Comput. Math. 19, 101–112 (2001) MathSciNetMATH

13.

Guo, B.-y., Shen, J.: Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Numer. Math. 86, 635–654 (2000) MathSciNetMATHCrossRef

14.

Guo, B.-y., Wang, T.-j.: Composite generalized Laguerre-Legendre spectral method with domain decomposition and its application to Fokker-Planck equation in an infinite channel. Math. Comput. 78, 129–151 (2009) MATHCrossRef

15.

Guo, B.-y., Xu, C.-l.: Mixed Laguerre-Legendre pseudospectral method for incompressible fluid flow in an infinite strip. Math. Comput. 72, 95–125 (2003) MathSciNet

16.

Guo, B.-y., Zhang, X.-y.: A new generalized Laguerre spectral approximation and its applications. J. Comput. Appl. Math. 181, 342–363 (2005) MathSciNetMATHCrossRef

17.

Guo, B.-y., Zhang, X.-y.: Spectral method for differential equations of degenerate type by using generalized Laguerre functions. Appl. Numer. Math. 57, 455–471 (2007) MathSciNetMATHCrossRef

18.

Guo, B.-y., Wang, L.-l., Wang, Z.-q.: Generalized Laguerre interpolation and pseudospectral method for unbounded domains. SIAM J. Numer. Anal. 43, 2567–2589 (2006) MathSciNetMATHCrossRef

19.

Guo, B.-y., Sun, T., Zhang, C.: Jacobi and Laguerre quasi-orthogonal approximations and related interpolations. Math. Comput. (in press)

20.

Karniadakis, G.E., Sherwin, S.J.: Spectral/hp Element Methods for CFD, 2nd edn. Oxford Univ. Press, Oxford (2005) CrossRef

21.

Shen, J.: Stable and efficient spectral methods in unbounded domains using Laguerre functions. SIAM J. Numer. Anal. 38, 1113–1133 (2000) MathSciNetMATHCrossRef

22.

Wang, L.-l., Guo, B.-y.: Interpolation approximations based on Gauss-Lobatto-Legendre-Birkhoff quadrature. J. Approx. Theory 161, 142–173 (2009) MathSciNetMATHCrossRef

23.

Xu, C.-l., Guo, B.-y.: Laguerre pseudospectral method for nonlinear partial differential equation. J. Comput. Math. 20, 413–428 (2002) MathSciNetMATH

Title: Domain Decomposition Spectral Method for Mixed Inhomogeneous Boundary Value Problems of High Order Differential Equations on Unbounded Domains
Authors: Chao Zhang
Ben-yu Guo
Publication date: 01-11-2012
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2/2012
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-012-9581-z

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 2/2012

A Fast Preconditioned Iterative Algorithm for the Electromagnetic Scattering from a Large Cavity

Method of Moving Frames to Solve Conservation Laws on Curved Surfaces

Image Approximations to Electrostatic Potentials in Layered Electrolytes/Dielectrics and an Ion-Channel Model

A Mixed and Nonconforming FEM with Nonmatching Meshes for a Coupled Stokes-Darcy Model

Local Convergence of the Lavrentiev Method for the Cauchy Problem via a Carleman Inequality

Erratum to: Method of Moving Frames to Solve Conservation Laws on Curved Surfaces

Premium Partner