FPM 2002, vol. 8, no. 1, pp. 301-305

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 M² - a [q(x)M - q''(x)] } y = -l My,
y (±1) = y' (±1) = 0,

where $M=d$ ²/dx² - a², $q(x)$ 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 $M$ ².

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