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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Main Authors: Solov´ev Sergey I., Solov´ev Pavel S., Chebakova Violetta Yu.
Format: Article
Language:English
Published: EDP Sciences 2017-01-01
Series:MATEC Web of Conferences
Online Access:https://doi.org/10.1051/matecconf/201712906014
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spelling 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
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AT chebakovaviolettayu finitedifferenceapproximationofelectronbalanceprobleminthestationaryhighfrequencyinductiondischarges
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