Numerical algorithms for one parabolic-elliptic problem
In this paper we solve numerically a parabolic-elliptic problem. Two finite difference schemes are proposed. The first scheme is a modification of the backward Euler algorithm and it requires to solve an elliptic problem at each time step. The spectral estimates of the obtained matrix are presented...
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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/32532 |
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| _version_ | 1832593138799083520 |
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| author | Raimondas Čiegis Remigijus Čiegis |
| author_facet | Raimondas Čiegis Remigijus Čiegis |
| author_sort | Raimondas Čiegis |
| collection | DOAJ |
| description |
In this paper we solve numerically a parabolic-elliptic problem. Two finite difference schemes are proposed. The first scheme is a modification of the backward Euler algorithm and it requires to solve an elliptic problem at each time step. The spectral estimates of the obtained matrix are presented. The second scheme is a modification of the stability-correction scheme. This scheme is used as a classical splitting scheme in the parabolic region of the problem definition and as a new iterative algorithm in the elliptic part of the problem. We prove the convergence of the proposed scheme.
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| format | Article |
| id | doaj-art-3b2c777805c44c2dba6220a03e99f48f |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2003-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-3b2c777805c44c2dba6220a03e99f48f2025-01-20T18:17:25ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2003-12-0143spec.10.15388/LMR.2003.32532Numerical algorithms for one parabolic-elliptic problemRaimondas Čiegis0Remigijus Čiegis1Vilnius Gediminas Technical UniversityVilnius University In this paper we solve numerically a parabolic-elliptic problem. Two finite difference schemes are proposed. The first scheme is a modification of the backward Euler algorithm and it requires to solve an elliptic problem at each time step. The spectral estimates of the obtained matrix are presented. The second scheme is a modification of the stability-correction scheme. This scheme is used as a classical splitting scheme in the parabolic region of the problem definition and as a new iterative algorithm in the elliptic part of the problem. We prove the convergence of the proposed scheme. https://www.journals.vu.lt/LMR/article/view/32532 |
| spellingShingle | Raimondas Čiegis Remigijus Čiegis Numerical algorithms for one parabolic-elliptic problem Lietuvos Matematikos Rinkinys |
| title | Numerical algorithms for one parabolic-elliptic problem |
| title_full | Numerical algorithms for one parabolic-elliptic problem |
| title_fullStr | Numerical algorithms for one parabolic-elliptic problem |
| title_full_unstemmed | Numerical algorithms for one parabolic-elliptic problem |
| title_short | Numerical algorithms for one parabolic-elliptic problem |
| title_sort | numerical algorithms for one parabolic elliptic problem |
| url | https://www.journals.vu.lt/LMR/article/view/32532 |
| work_keys_str_mv | AT raimondasciegis numericalalgorithmsforoneparabolicellipticproblem AT remigijusciegis numericalalgorithmsforoneparabolicellipticproblem |