Numerical method for a Schrödinger problem with amplification process
In this paper we consider one Schrödinger problem which describes a signal propagation in optical fibers. The stability of symmetrical finite difference scheme is investigated in the L2 norm. It is proved that the scheme becomes unstable if the signal is periodically amplified along the fiber. A mo...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
1999-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/35668 |
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| _version_ | 1825197164687523840 |
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| author | Raimondas Čiegis Genė Kairytė Violeta Pakalnytė |
| author_facet | Raimondas Čiegis Genė Kairytė Violeta Pakalnytė |
| author_sort | Raimondas Čiegis |
| collection | DOAJ |
| description |
In this paper we consider one Schrödinger problem which describes a signal propagation in optical fibers. The stability of symmetrical finite difference scheme is investigated in the L2 norm. It is proved that the scheme becomes unstable if the signal is periodically amplified along the fiber. A modification of the symmetrical scheme and one splitting scheme are proposed to solve the given problem.
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| format | Article |
| id | doaj-art-60a8defeb6b94157ba0ff2285267d7c5 |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 1999-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-60a8defeb6b94157ba0ff2285267d7c52025-02-11T18:15:14ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X1999-12-0139III10.15388/LMD.1999.35668Numerical method for a Schrödinger problem with amplification processRaimondas Čiegis0Genė Kairytė1Violeta Pakalnytė2Vilnius Gediminas Technical UniversityInstitute of Mathematics and InformaticsInstitute of Mathematics and Informatics In this paper we consider one Schrödinger problem which describes a signal propagation in optical fibers. The stability of symmetrical finite difference scheme is investigated in the L2 norm. It is proved that the scheme becomes unstable if the signal is periodically amplified along the fiber. A modification of the symmetrical scheme and one splitting scheme are proposed to solve the given problem. https://www.zurnalai.vu.lt/LMR/article/view/35668 |
| spellingShingle | Raimondas Čiegis Genė Kairytė Violeta Pakalnytė Numerical method for a Schrödinger problem with amplification process Lietuvos Matematikos Rinkinys |
| title | Numerical method for a Schrödinger problem with amplification process |
| title_full | Numerical method for a Schrödinger problem with amplification process |
| title_fullStr | Numerical method for a Schrödinger problem with amplification process |
| title_full_unstemmed | Numerical method for a Schrödinger problem with amplification process |
| title_short | Numerical method for a Schrödinger problem with amplification process |
| title_sort | numerical method for a schrodinger problem with amplification process |
| url | https://www.zurnalai.vu.lt/LMR/article/view/35668 |
| work_keys_str_mv | AT raimondasciegis numericalmethodforaschrodingerproblemwithamplificationprocess AT genekairyte numericalmethodforaschrodingerproblemwithamplificationprocess AT violetapakalnyte numericalmethodforaschrodingerproblemwithamplificationprocess |