FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 1, PAGES 301-305

**On the computing of the eigenvalues of the Orr--Sommerfeld problem**

M. I. Neiman-zade

A. A. Shkalikov

Abstract

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The paper deals with the Orr--Sommerfeld problem

{ (iR)^{-1} M^{2}
- a
[q(x)M - q''(x)] } y =
-l My,

y (±1) =
y' (±1) = 0,
where $M=d2/dx2$ - a^{2},
$q(x)$ is the
velocity profile, $R$ and $$a 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 $M2$.

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published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k02/k021/k02123h.htm

Last modified: July 8, 2002