A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup
The aim of this work is to study a semidiscrete Crank-Nicolson type scheme in order to approximate numerically the Dirichlet-to-Neumann semigroup. We construct an approximating family of operators for the Dirichlet-to-Neumann semigroup, which satisfies the assumptions of Chernoff’s product formula,...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/429641 |
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| _version_ | 1832551946392698880 |
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| author | Rola Ali Ahmad Toufic El Arwadi Houssam Chrayteh Jean-Marc Sac-Epée |
| author_facet | Rola Ali Ahmad Toufic El Arwadi Houssam Chrayteh Jean-Marc Sac-Epée |
| author_sort | Rola Ali Ahmad |
| collection | DOAJ |
| description | The aim of this work is to study a semidiscrete Crank-Nicolson type scheme in order to approximate numerically the Dirichlet-to-Neumann semigroup. We construct an approximating family of operators for the Dirichlet-to-Neumann semigroup, which satisfies the assumptions of Chernoff’s product formula, and consequently the Crank-Nicolson scheme converges to the exact solution. Finally, we write a P1 finite element scheme for the problem, and we illustrate this convergence by means of a FreeFem++ implementation. |
| format | Article |
| id | doaj-art-4e2553be69c14413b0eefd067eb19d3b |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4e2553be69c14413b0eefd067eb19d3b2025-02-03T06:00:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/429641429641A Crank-Nicolson Scheme for the Dirichlet-to-Neumann SemigroupRola Ali Ahmad0Toufic El Arwadi1Houssam Chrayteh2Jean-Marc Sac-Epée3Department of Mathematics, Faculty of Science, Beirut Arab University, P.O. Box 11-5020, Beirut, LebanonDepartment of Mathematics, Faculty of Science, Beirut Arab University, P.O. Box 11-5020, Beirut, LebanonDepartment of Mathematics, Faculty of Science, Beirut Arab University, P.O. Box 11-5020, Beirut, LebanonInstitut Élie Cartan de Lorraine, UMR 7502, Université de Lorraine, 57 045 Metz, FranceThe aim of this work is to study a semidiscrete Crank-Nicolson type scheme in order to approximate numerically the Dirichlet-to-Neumann semigroup. We construct an approximating family of operators for the Dirichlet-to-Neumann semigroup, which satisfies the assumptions of Chernoff’s product formula, and consequently the Crank-Nicolson scheme converges to the exact solution. Finally, we write a P1 finite element scheme for the problem, and we illustrate this convergence by means of a FreeFem++ implementation.http://dx.doi.org/10.1155/2015/429641 |
| spellingShingle | Rola Ali Ahmad Toufic El Arwadi Houssam Chrayteh Jean-Marc Sac-Epée A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup Journal of Applied Mathematics |
| title | A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup |
| title_full | A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup |
| title_fullStr | A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup |
| title_full_unstemmed | A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup |
| title_short | A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup |
| title_sort | crank nicolson scheme for the dirichlet to neumann semigroup |
| url | http://dx.doi.org/10.1155/2015/429641 |
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