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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0365-0359 1825-1242 |