| Issue |
MATEC Web Conf.
Volume 129, 2017
International Conference on Modern Trends in Manufacturing Technologies and Equipment (ICMTMTE 2017)
|
|
|---|---|---|
| Article Number | 06014 | |
| Number of page(s) | 4 | |
| Section | Other Related Topics | |
| DOI | https://doi.org/10.1051/matecconf/201712906014 | |
| Published online | 07 November 2017 | |
Finite difference approximation of electron balance problem in the stationary high-frequency induction discharges
Kazan Federal University, 18 Kremlevskaya Street, Kazan, 420008, Russian Federation
* Corresponding Author: sergei.solovyev@kpfu.ru
The problem of finding the minimal eigenvalue corresponding to a positive eigenfunction of the nonlinear eigenvalue problem for the ordinary differential equation with coefficients depending on a spectral parameter is investigated. This problem arises in modeling the plasma of radio-frequency discharge at reduced pressures. The original differential eigenvalue problem is approximated by the finite difference method on a uniform grid. A sufficient condition for the existence of a minimal eigenvalue corresponding to a positive eigenfunction of the finite difference nonlinear eigenvalue problem is established. Error estimates for the approximate eigenvalue and the corresponding approximate positive eigenfunction are proved. Investigations of this paper generalize well known results for eigenvalue problems with linear dependence on the spectral parameter.
© The Authors, published by EDP Sciences, 2017
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
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