Comparative analysis by means of finite differences and DM methods for linearized problem of gyrotrons

The problem of Schrödinger equation with complex boundary conditions for modelling a motion of electrons in gyrotrons is considered. Numerical results obtained by using Fourier, Finite Differences (FD) and Degenerate Matrices (DM) methods are compared in the simplest case. For DM methods they are an...

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Main Authors: T. Cirulis, H. Kalis, O. Lietuvietis
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2004-06-01
Series:Mathematical Modelling and Analysis
Subjects:
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/9715
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author T. Cirulis
H. Kalis
O. Lietuvietis
author_facet T. Cirulis
H. Kalis
O. Lietuvietis
author_sort T. Cirulis
collection DOAJ
description The problem of Schrödinger equation with complex boundary conditions for modelling a motion of electrons in gyrotrons is considered. Numerical results obtained by using Fourier, Finite Differences (FD) and Degenerate Matrices (DM) methods are compared in the simplest case. For DM methods they are analysed also in more general cases, when FD can not be applied because of fast oscillations of the solution. Baigtinių skirtumų ir DM metodo lygiamoji analizė linearizuotam girotrono uždaviniui Santrauka Nagrinejamas kraštinis uždavinys Šredingerio lygčiai, aprašantis elektronu judejima girotrone. Darbe lyginami ir analizuojami Furje, baigtiniu skirtumu ir degeneruotu matricu (DM) metodais gauti skaitiniai rezultatai. Aptartas metodo taikymas greitu osciliaciju atveju. First Published Online: 14 Oct 2010
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spelling doaj.art-06682104d1d94a4c8d2b0b10d70263722022-12-21T21:14:48ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102004-06-019210.3846/13926292.2004.9637247Comparative analysis by means of finite differences and DM methods for linearized problem of gyrotronsT. Cirulis0H. Kalis1O. Lietuvietis2Institute of Mathematics , Latvian Academy of Sciences and University of Latvia , Akademijas laukums 1, Riga, LV‐1524, LatviaInstitute of Mathematics , Latvian Academy of Sciences and University of Latvia , Akademijas laukums 1, Riga, LV‐1524, LatviaInstitute of Mathematics , Latvian Academy of Sciences and University of Latvia , Akademijas laukums 1, Riga, LV‐1524, LatviaThe problem of Schrödinger equation with complex boundary conditions for modelling a motion of electrons in gyrotrons is considered. Numerical results obtained by using Fourier, Finite Differences (FD) and Degenerate Matrices (DM) methods are compared in the simplest case. For DM methods they are analysed also in more general cases, when FD can not be applied because of fast oscillations of the solution. Baigtinių skirtumų ir DM metodo lygiamoji analizė linearizuotam girotrono uždaviniui Santrauka Nagrinejamas kraštinis uždavinys Šredingerio lygčiai, aprašantis elektronu judejima girotrone. Darbe lyginami ir analizuojami Furje, baigtiniu skirtumu ir degeneruotu matricu (DM) metodais gauti skaitiniai rezultatai. Aptartas metodo taikymas greitu osciliaciju atveju. First Published Online: 14 Oct 2010https://journals.vgtu.lt/index.php/MMA/article/view/9715gyrotronSchrödinger equationcomplex boundary conditionsFourier methodfinite differencesdegenerate matrices method
spellingShingle T. Cirulis
H. Kalis
O. Lietuvietis
Comparative analysis by means of finite differences and DM methods for linearized problem of gyrotrons
Mathematical Modelling and Analysis
gyrotron
Schrödinger equation
complex boundary conditions
Fourier method
finite differences
degenerate matrices method
title Comparative analysis by means of finite differences and DM methods for linearized problem of gyrotrons
title_full Comparative analysis by means of finite differences and DM methods for linearized problem of gyrotrons
title_fullStr Comparative analysis by means of finite differences and DM methods for linearized problem of gyrotrons
title_full_unstemmed Comparative analysis by means of finite differences and DM methods for linearized problem of gyrotrons
title_short Comparative analysis by means of finite differences and DM methods for linearized problem of gyrotrons
title_sort comparative analysis by means of finite differences and dm methods for linearized problem of gyrotrons
topic gyrotron
Schrödinger equation
complex boundary conditions
Fourier method
finite differences
degenerate matrices method
url https://journals.vgtu.lt/index.php/MMA/article/view/9715
work_keys_str_mv AT tcirulis comparativeanalysisbymeansoffinitedifferencesanddmmethodsforlinearizedproblemofgyrotrons
AT hkalis comparativeanalysisbymeansoffinitedifferencesanddmmethodsforlinearizedproblemofgyrotrons
AT olietuvietis comparativeanalysisbymeansoffinitedifferencesanddmmethodsforlinearizedproblemofgyrotrons