A modified tau spectral method that eliminates spurious eigenvalues

David R. Gardner; Steven A. Trogdon; Rod W. Douglass

doi:10.1016/0021-9991(89)90093-4

A modified tau spectral method that eliminates spurious eigenvalues

David R. Gardner, Steven A. Trogdon, Rod W. Douglass

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

56 Scopus citations

Abstract

A modified tau spectral method is presented which eliminates the spurious eigenvalues produced by the usual tau method. The modified tau method essentially involves an appropriate factorization of the differential operators in the eigenvalue problem. It is developed for eigenvalue problems posed as single differential equations or as systems of such equations. Several eigenvalue problems are solved using both the usual and modified Chebyshev-tau methods, including the Orr-Sommerfeld stability equation for plane Poiseuille flow. The convergence of the modified tau method is shown to be at least as rapid as that of the usual tau method. The use of the tau coefficients in indicating convergence is also discussed.

Original language	English (US)
Pages (from-to)	137-167
Number of pages	31
Journal	Journal of Computational Physics
Volume	80
Issue number	1
DOIs	https://doi.org/10.1016/0021-9991(89)90093-4
State	Published - Jan 1989

Bibliographical note

Funding Information:
This work was supported by the Mechanical Engineering Department of the University of Nebraska-Lincoln and by the National ScienceF oundationt hroughG rant CBT-8612427T. his support is gratefullya cknowledged.

Access

10.1016/0021-9991(89)90093-4

OpenUrl availability

Full text

Cite this

@article{e2e1349e4aef4f979b1ee0e6c46592bf,

title = "A modified tau spectral method that eliminates spurious eigenvalues",

abstract = "A modified tau spectral method is presented which eliminates the spurious eigenvalues produced by the usual tau method. The modified tau method essentially involves an appropriate factorization of the differential operators in the eigenvalue problem. It is developed for eigenvalue problems posed as single differential equations or as systems of such equations. Several eigenvalue problems are solved using both the usual and modified Chebyshev-tau methods, including the Orr-Sommerfeld stability equation for plane Poiseuille flow. The convergence of the modified tau method is shown to be at least as rapid as that of the usual tau method. The use of the tau coefficients in indicating convergence is also discussed.",

author = "Gardner, {David R.} and Trogdon, {Steven A.} and Douglass, {Rod W.}",

note = "Funding Information: This work was supported by the Mechanical Engineering Department of the University of Nebraska-Lincoln and by the National ScienceF oundationt hroughG rant CBT-8612427T. his support is gratefullya cknowledged.",

year = "1989",

month = jan,

doi = "10.1016/0021-9991(89)90093-4",

language = "English (US)",

volume = "80",

pages = "137--167",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - A modified tau spectral method that eliminates spurious eigenvalues

AU - Gardner, David R.

AU - Trogdon, Steven A.

AU - Douglass, Rod W.

N1 - Funding Information: This work was supported by the Mechanical Engineering Department of the University of Nebraska-Lincoln and by the National ScienceF oundationt hroughG rant CBT-8612427T. his support is gratefullya cknowledged.

PY - 1989/1

Y1 - 1989/1

N2 - A modified tau spectral method is presented which eliminates the spurious eigenvalues produced by the usual tau method. The modified tau method essentially involves an appropriate factorization of the differential operators in the eigenvalue problem. It is developed for eigenvalue problems posed as single differential equations or as systems of such equations. Several eigenvalue problems are solved using both the usual and modified Chebyshev-tau methods, including the Orr-Sommerfeld stability equation for plane Poiseuille flow. The convergence of the modified tau method is shown to be at least as rapid as that of the usual tau method. The use of the tau coefficients in indicating convergence is also discussed.

AB - A modified tau spectral method is presented which eliminates the spurious eigenvalues produced by the usual tau method. The modified tau method essentially involves an appropriate factorization of the differential operators in the eigenvalue problem. It is developed for eigenvalue problems posed as single differential equations or as systems of such equations. Several eigenvalue problems are solved using both the usual and modified Chebyshev-tau methods, including the Orr-Sommerfeld stability equation for plane Poiseuille flow. The convergence of the modified tau method is shown to be at least as rapid as that of the usual tau method. The use of the tau coefficients in indicating convergence is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=45149146149&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45149146149&partnerID=8YFLogxK

U2 - 10.1016/0021-9991(89)90093-4

DO - 10.1016/0021-9991(89)90093-4

M3 - Article

AN - SCOPUS:45149146149

SN - 0021-9991

VL - 80

SP - 137

EP - 167

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

A modified tau spectral method that eliminates spurious eigenvalues

Abstract

Bibliographical note

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this