Finite difference approximation of electron balance problem in the stationary high-frequency induction discharges
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 discha...
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2017-01-01
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Series: | MATEC Web of Conferences |
Online Access: | https://doi.org/10.1051/matecconf/201712906014 |
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doaj-38e9b1913e154f4bb0f11421a739c0332021-08-11T14:29:44ZengEDP SciencesMATEC Web of Conferences2261-236X2017-01-011290601410.1051/matecconf/201712906014matecconf_icmtmte2017_06014Finite difference approximation of electron balance problem in the stationary high-frequency induction dischargesSolov´ev Sergey I.Solov´ev Pavel S.Chebakova Violetta Yu.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.https://doi.org/10.1051/matecconf/201712906014 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Solov´ev Sergey I. Solov´ev Pavel S. Chebakova Violetta Yu. |
spellingShingle |
Solov´ev Sergey I. Solov´ev Pavel S. Chebakova Violetta Yu. Finite difference approximation of electron balance problem in the stationary high-frequency induction discharges MATEC Web of Conferences |
author_facet |
Solov´ev Sergey I. Solov´ev Pavel S. Chebakova Violetta Yu. |
author_sort |
Solov´ev Sergey I. |
title |
Finite difference approximation of electron balance problem in the stationary high-frequency induction discharges |
title_short |
Finite difference approximation of electron balance problem in the stationary high-frequency induction discharges |
title_full |
Finite difference approximation of electron balance problem in the stationary high-frequency induction discharges |
title_fullStr |
Finite difference approximation of electron balance problem in the stationary high-frequency induction discharges |
title_full_unstemmed |
Finite difference approximation of electron balance problem in the stationary high-frequency induction discharges |
title_sort |
finite difference approximation of electron balance problem in the stationary high-frequency induction discharges |
publisher |
EDP Sciences |
series |
MATEC Web of Conferences |
issn |
2261-236X |
publishDate |
2017-01-01 |
description |
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. |
url |
https://doi.org/10.1051/matecconf/201712906014 |
work_keys_str_mv |
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1721210793006989312 |