Two finite difference methods for a nonlinear BVP arising in physical oceanography
In this paper we define two finite difference methods for a nonlinear boundary value problem on infinite interval. In particular, we report and compare the numerical results for an ocean circulation model obtained by the free boundary approach and a treatment of the problem on the original semi-infi...
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| Format: | Article |
| Language: | English |
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Accademia Peloritana dei Pericolanti
2018-10-01
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| Series: | Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| Online Access: |
http://dx.doi.org/10.1478/AAPP.962A3
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| _version_ | 1819236546288549888 |
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| author | Riccardo Fazio Alessandra Jannelli |
| author_facet | Riccardo Fazio Alessandra Jannelli |
| author_sort | Riccardo Fazio |
| collection | DOAJ |
| description | In this paper we define two finite difference methods for a nonlinear boundary value problem on infinite interval. In particular, we report and compare the numerical results for an ocean circulation model obtained by the free boundary approach and a treatment of the problem on the original semi-infinite domain by introducing a quasi-uniform grid. In the first case we apply finite difference formulae on a uniform grid and in the second case we use non-standard finite differences on a quasi-uniform grid. We point out how both approaches represent reliable ways to solve boundary value problems defined on semi-infinite intervals. In fact, both approaches overcome the need to define a priori, or find by trials, a suitable truncated boundary used by the classical numerical treatment of boundary value problems defined on a semi-infinite interval. Finally, the reported numerical results allow to point out how the finite difference method with a quasi-uniform grid is the least demanding approach between the two and that the free boundary approach provides a more reliable formulation than the classical truncated boundary one. |
| first_indexed | 2024-12-23T13:06:09Z |
| format | Article |
| id | doaj.art-ba854903156a4e6fb35061f548499062 |
| institution | Directory Open Access Journal |
| issn | 0365-0359 1825-1242 |
| language | English |
| last_indexed | 2024-12-23T13:06:09Z |
| publishDate | 2018-10-01 |
| publisher | Accademia Peloritana dei Pericolanti |
| record_format | Article |
| series | Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| spelling | doaj.art-ba854903156a4e6fb35061f5484990622022-12-21T17:45:53ZengAccademia Peloritana dei PericolantiAtti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali0365-03591825-12422018-10-01962A310.1478/AAPP.962A3AAPP.962A3Two finite difference methods for a nonlinear BVP arising in physical oceanographyRiccardo FazioAlessandra JannelliIn this paper we define two finite difference methods for a nonlinear boundary value problem on infinite interval. In particular, we report and compare the numerical results for an ocean circulation model obtained by the free boundary approach and a treatment of the problem on the original semi-infinite domain by introducing a quasi-uniform grid. In the first case we apply finite difference formulae on a uniform grid and in the second case we use non-standard finite differences on a quasi-uniform grid. We point out how both approaches represent reliable ways to solve boundary value problems defined on semi-infinite intervals. In fact, both approaches overcome the need to define a priori, or find by trials, a suitable truncated boundary used by the classical numerical treatment of boundary value problems defined on a semi-infinite interval. Finally, the reported numerical results allow to point out how the finite difference method with a quasi-uniform grid is the least demanding approach between the two and that the free boundary approach provides a more reliable formulation than the classical truncated boundary one. http://dx.doi.org/10.1478/AAPP.962A3 |
| spellingShingle | Riccardo Fazio Alessandra Jannelli Two finite difference methods for a nonlinear BVP arising in physical oceanography Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| title | Two finite difference methods for a nonlinear BVP arising in physical oceanography |
| title_full | Two finite difference methods for a nonlinear BVP arising in physical oceanography |
| title_fullStr | Two finite difference methods for a nonlinear BVP arising in physical oceanography |
| title_full_unstemmed | Two finite difference methods for a nonlinear BVP arising in physical oceanography |
| title_short | Two finite difference methods for a nonlinear BVP arising in physical oceanography |
| title_sort | two finite difference methods for a nonlinear bvp arising in physical oceanography |
| url |
http://dx.doi.org/10.1478/AAPP.962A3
|
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