The calculation of eigenvalues for the stationary perturbation of Poiseuille flow using initial value methods
type: Item
instance of: scholarly article
title: The calculation of eigenvalues for the stationary perturbation of Poiseuille flow using initial value methods
zbMATH Open document ID: 0598.76031
DOI: 10.1016/0022-247X(84)90056-8
author: J. S. Bramley
author: S. C. R. Dennis
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: The authors [J. Comput. Phys. 47, 179-198 (1982; Zbl 0493.76025)] obtained the eigenvalues of a stationary perturbation of Poiseuille flow for the viscous flow in a straight channel and solved the problem by a spectral method using Chebyshev series. The present paper is an extension and solves the same problem using initial-value methods: Riccati transformation, the compound matrix method, and orthogonalization. It is possible to calculate additional complex eigenvalues using initial value methods and these eigenvalues are presented. The spectral method gives the eigenvalues without searching on a real line or over a complex plane.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 3965664
zbMATH Keywords: eigenvalues
zbMATH Keywords: stationary perturbation
zbMATH Keywords: Poiseuille flow
zbMATH Keywords: straight channel
zbMATH Keywords: spectral method
zbMATH Keywords: Chebyshev series
zbMATH Keywords: initial-value methods
zbMATH Keywords: Riccati transformation
zbMATH Keywords: compound matrix method
zbMATH Keywords: orthogonalization
zbMATH Keywords: complex eigenvalues
MaRDI profile type: Publication
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full work available at URL: 0022-247x(84)90056-8
OpenAlex ID: W1989717053
description: scientific article; zbMATH DE number 3965664