Chebyshev iteration for the problem with nonlocal boundary condition
We considered Poisson differential equation with Dirichlet boundary conditions and one nonlocal boundary condition. Finite-difference scheme was investigated for this problem. The eigenvalues of such problem depend on few parameters in the nonlocal boundary condition. The convergence rate for Cheby...
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| Language: | English |
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Vilnius University Press
2004-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
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| Online Access: | https://www.journals.vu.lt/LMR/article/view/15313 |
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| _version_ | 1832593170466078720 |
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| author | Mifodijus Sapagovas Artūras Štikonas Olga Štikonienė |
| author_facet | Mifodijus Sapagovas Artūras Štikonas Olga Štikonienė |
| author_sort | Mifodijus Sapagovas |
| collection | DOAJ |
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We considered Poisson differential equation with Dirichlet boundary conditions and one nonlocal boundary condition. Finite-difference scheme was investigated for this problem. The eigenvalues of such problem depend on few parameters in the nonlocal boundary condition. The convergence rate for Cheby-shev iterations depends on the number of the discrete mesh points. The convergence is more faster when the maximal eigenvalue of the corresponding nonsimmetric matrix is simple.
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| format | Article |
| id | doaj-art-0be8e8ba34f148ec82851369c2a1d1ed |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2004-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-0be8e8ba34f148ec82851369c2a1d1ed2025-01-20T18:17:14ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2004-12-0144spec.10.15388/LMR.2004.15313Chebyshev iteration for the problem with nonlocal boundary conditionMifodijus Sapagovas0Artūras Štikonas1https://orcid.org/0000-0002-5872-5501Olga Štikonienė2Vilnius UniversityVilnius UniversityVilnius University We considered Poisson differential equation with Dirichlet boundary conditions and one nonlocal boundary condition. Finite-difference scheme was investigated for this problem. The eigenvalues of such problem depend on few parameters in the nonlocal boundary condition. The convergence rate for Cheby-shev iterations depends on the number of the discrete mesh points. The convergence is more faster when the maximal eigenvalue of the corresponding nonsimmetric matrix is simple. https://www.journals.vu.lt/LMR/article/view/15313Poisson differential equationnonlocal boundary conditionfinite difference schemeChebyshev iteration |
| spellingShingle | Mifodijus Sapagovas Artūras Štikonas Olga Štikonienė Chebyshev iteration for the problem with nonlocal boundary condition Lietuvos Matematikos Rinkinys Poisson differential equation nonlocal boundary condition finite difference scheme Chebyshev iteration |
| title | Chebyshev iteration for the problem with nonlocal boundary condition |
| title_full | Chebyshev iteration for the problem with nonlocal boundary condition |
| title_fullStr | Chebyshev iteration for the problem with nonlocal boundary condition |
| title_full_unstemmed | Chebyshev iteration for the problem with nonlocal boundary condition |
| title_short | Chebyshev iteration for the problem with nonlocal boundary condition |
| title_sort | chebyshev iteration for the problem with nonlocal boundary condition |
| topic | Poisson differential equation nonlocal boundary condition finite difference scheme Chebyshev iteration |
| url | https://www.journals.vu.lt/LMR/article/view/15313 |
| work_keys_str_mv | AT mifodijussapagovas chebysheviterationfortheproblemwithnonlocalboundarycondition AT arturasstikonas chebysheviterationfortheproblemwithnonlocalboundarycondition AT olgastikoniene chebysheviterationfortheproblemwithnonlocalboundarycondition |