Stationary problems with various nonlocal boundary conditions
In this paper we investigate one-dimensional stationary differential problems with various nonlocal boundary conditions and finite difference schemes for them. The boundary conditions of the first, second and third type are considered and nonlocal part of those boundary conditions can be integral t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2003-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.journals.vu.lt/LMR/article/view/15316 |
| _version_ | 1797194431323963392 |
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| author | Artūras Štikonas Olga Štikonienė Sigita Pečiulytė |
| author_facet | Artūras Štikonas Olga Štikonienė Sigita Pečiulytė |
| author_sort | Artūras Štikonas |
| collection | DOAJ |
| description |
In this paper we investigate one-dimensional stationary differential problems with various nonlocal boundary conditions and finite difference schemes for them. The boundary conditions of the first, second and third type are considered and nonlocal part of those boundary conditions can be integral type or Samarskii and Bitsadze type. The base idea is to use fundamental solutions of the stationary problems with classical boundary conditions. We find necessary and sufficient solvability conditions for such problems. Stability estimates are proved in the maximum norm. The convergence of the second order finite difference schemes is proved.
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| first_indexed | 2024-03-07T15:40:09Z |
| format | Article |
| id | doaj.art-f0763b879d4c415992278c2048c3f688 |
| institution | Directory Open Access Journal |
| issn | 0132-2818 2335-898X |
| language | English |
| last_indexed | 2024-04-24T05:56:10Z |
| publishDate | 2003-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj.art-f0763b879d4c415992278c2048c3f6882024-04-23T09:03:59ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2003-12-0143spec.10.15388/LMR.2003.15316Stationary problems with various nonlocal boundary conditionsArtūras Štikonas0https://orcid.org/0000-0002-5872-5501Olga Štikonienė1Sigita Pečiulytė2Vilnius UniversityVilnius UniversityVytautas Magnus University In this paper we investigate one-dimensional stationary differential problems with various nonlocal boundary conditions and finite difference schemes for them. The boundary conditions of the first, second and third type are considered and nonlocal part of those boundary conditions can be integral type or Samarskii and Bitsadze type. The base idea is to use fundamental solutions of the stationary problems with classical boundary conditions. We find necessary and sufficient solvability conditions for such problems. Stability estimates are proved in the maximum norm. The convergence of the second order finite difference schemes is proved. https://www.journals.vu.lt/LMR/article/view/15316 |
| spellingShingle | Artūras Štikonas Olga Štikonienė Sigita Pečiulytė Stationary problems with various nonlocal boundary conditions Lietuvos Matematikos Rinkinys |
| title | Stationary problems with various nonlocal boundary conditions |
| title_full | Stationary problems with various nonlocal boundary conditions |
| title_fullStr | Stationary problems with various nonlocal boundary conditions |
| title_full_unstemmed | Stationary problems with various nonlocal boundary conditions |
| title_short | Stationary problems with various nonlocal boundary conditions |
| title_sort | stationary problems with various nonlocal boundary conditions |
| url | https://www.journals.vu.lt/LMR/article/view/15316 |
| work_keys_str_mv | AT arturasstikonas stationaryproblemswithvariousnonlocalboundaryconditions AT olgastikoniene stationaryproblemswithvariousnonlocalboundaryconditions AT sigitapeciulyte stationaryproblemswithvariousnonlocalboundaryconditions |