Removal of spurious modes encountered in solving stability problems by spectral methods.

*(English)*Zbl 0612.65049An important application of Chebyshev spectral methods is found in the solution of hydrodynamic stability eigenvalue problems. Unfortunately, along with the highly accurate computed values of the true modes, there appear spurious unstable modes with large growth rates whose magnitude increases with an increase of the size of the truncated algebraic system of equations. One way to eliminate the spurious roots in hydrodynamics (if they occur) is to use separate expansions for the vorticity and the stream function. However, the size of the resulting algebraic system essentially doubles. In this paper we develop an alternative technique based on the Galerkin method which results in no increase in the size of the algebraic system.

##### MSC:

65L15 | Numerical solution of eigenvalue problems involving ordinary differential equations |

65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |

34L99 | Ordinary differential operators |

##### Keywords:

Orr-Sommerfeld equation; Chebyshev spectral methods; hydrodynamic stability eigenvalue problems; spurious unstable modes; Galerkin method
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##### References:

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