%0 Journal Article %1 gardner1989modified %A Gardner, D. R. %A Trogdon, S. A. %A Douglass, R. W. %D 1989 %J Journal of Computational Physics %K 76e05-parallel-shear-flows 76m22-spectral-methods-in-fluid-mechanics usyd %N 1 %P 137--167 %T A Modified Tau Spectral Method that Eliminates Spurious Eigenvalues %U https://www.sciencedirect.com/science/article/pii/0021999189900934 %V 80 %X 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.

@article{gardner1989modified, 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.}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Gardner, D. R. and Trogdon, S. A. and Douglass, R. W.}, biburl = {https://www.bibsonomy.org/bibtex/2ee4805f63cbe6c20edcbd3c4c5be4641/gdmcbain}, citeulike-article-id = {2441414}, interhash = {3c1734c51bdfcb6b071c0a40c08f67f2}, intrahash = {ee4805f63cbe6c20edcbd3c4c5be4641}, journal = {Journal of Computational Physics}, keywords = {76e05-parallel-shear-flows 76m22-spectral-methods-in-fluid-mechanics usyd}, number = 1, pages = {137--167}, posted-at = {2008-02-28 10:10:17}, priority = {2}, timestamp = {2020-07-08T02:53:08.000+0200}, title = {A Modified Tau Spectral Method that Eliminates Spurious Eigenvalues}, url = {https://www.sciencedirect.com/science/article/pii/0021999189900934}, volume = 80, year = 1989 }