FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 1, PAGES 301-305
M. I. Neiman-zade
A. A. Shkalikov
Abstract
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The paper deals with the Orr--Sommerfeld problem
\begin{align*}
& \{ (iR)^{-1} M^2 - \alpha [q(x)M - q''(x)] \} y = -\lambda My,\\
& y(\pm 1) = y'(\pm1) = 0,
\end{align*}
where $M = d^2/dx^2 - \alpha^2$ ,
$q(x)$ is the velocity profile,
$R$ and $\alpha$ are Reynolds and wave numbers, respectively.
We approve the Galerkin method to compute the eigenvalues
of this problem provided that the basis for the method consists of the
eigenfunctions of the operator $M^2$ .
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Last modified: July 8, 2002