The Origin and Nature of Spurious Eigenvalues in the Spectral Tau Method
作者： Paul T. Dawkins , Steven R. Dunbar , Rod W. Douglass
关键词:
摘要: The Chebyshev?tau spectral method for approximating eigenvalues of boundary value problems may produce spurious with large positive real parts, even when all true the problem are known to have negative parts. We explain origin and nature “spurious eigenvalues” in an example problem. explanation will demonstrate that approximation infinite a nearby generalized eigenvalue
harvard.edu
acm.org
osti.gov
elsevier.com
sci-hub.se 参考文章(19)
David R Gardner, Steven A Trogdon, Rod W Douglass, A modified tau spectral method that eliminated spurious eigenvalues Journal of Computational Physics. ,vol. 80, pp. 137- 167 ,(1989) , 10.1016/0021-9991(89)90093-4
J. B. McGuire, Interacting Fermions in One Dimension. II. Attractive Potential Journal of Mathematical Physics. ,vol. 7, pp. 123- 132 ,(1966) , 10.1063/1.1704798
B. Straughan, D.W. Walker, Two Very Accurate and Efficient Methods for Computing Eigenvalues and Eigenfunctions in Porous Convection Problems Journal of Computational Physics. ,vol. 127, pp. 128- 141 ,(1996) , 10.1006/JCPH.1996.0163
Weizhang Huang, David M. Sloan, The pseudospectral method for solving differential eigenvalue problems Journal of Computational Physics. ,vol. 111, pp. 399- 409 ,(1994) , 10.1006/JCPH.1994.1073
Eduardo L. Ortiz, The Tau Method SIAM Journal on Numerical Analysis. ,vol. 6, pp. 480- 492 ,(1969) , 10.1137/0706044
L. Fox, Chebyshev Methods for Ordinary Differential Equations The Computer Journal. ,vol. 4, pp. 318- 331 ,(1962) , 10.1093/COMJNL/4.4.318
Steven A. Orszag, Accurate solution of the Orr–Sommerfeld stability equation Journal of Fluid Mechanics. ,vol. 50, pp. 689- 703 ,(1971) , 10.1017/S0022112071002842
C Lanczos, Trigonometric Interpolation of Empirical and Analytical Functions Journal of Mathematics and Physics. ,vol. 17, pp. 123- 199 ,(1938) , 10.1002/SAPM1938171123
D. H. Sattinger, Stability and bifurcation Lecture Notes in Mathematics. pp. 37- 69 ,(1979) , 10.1007/BFB0087459
B. Roux, P. Bontoux, B. Brenier, Comparaison des méthodes Tau-Chebyshev et Galerkin dans l'étude de stabilité des mouvements de convection naturelle. Problème des valeurs propres parasites Journal de mécanique théorique et appliquée. ,vol. 5, pp. 95- 119 ,(1986)