A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation
We consider three level difference replacements of parabolic equations focusing on the heat equation in two space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an alternating direction implicit (ADI) method. Using the well known fact of the parabolic-ellipti...
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2023
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| author | Sahimi M.S. Mansor N.A. Nor N.M. Nusi N.M. #Not Available# N. Alias |
| author2 | 35561342900 |
| author_facet | 35561342900 Sahimi M.S. Mansor N.A. Nor N.M. Nusi N.M. #Not Available# N. Alias |
| author_sort | Sahimi M.S. |
| building | UNITEN Library |
| collection | Institutional Repository |
| content_provider | Universiti Tenaga Nasional |
| content_source | UNITEN Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | We consider three level difference replacements of parabolic equations focusing on the heat equation in two space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an alternating direction implicit (ADI) method. Using the well known fact of the parabolic-elliptic correspondence, we shall derive a two stage iterative procedure employing a fractional splitting strategy applied alternately at each intermediate time step to the one dimensional heat equation. As the basis of derivation is the unconditionally stable (4,2) accurate ADI scheme, this method is convergent, computationally stable and highly accurate. � 2006 Inderscience Enterprises Ltd. |
| format | Article |
| id | my.uniten.dspace-29773 |
| institution | Universiti Tenaga Nasional |
| publishDate | 2023 |
| record_format | dspace |
| spelling | my.uniten.dspace-297732023-12-28T16:57:37Z A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation Sahimi M.S. Mansor N.A. Nor N.M. Nusi N.M. #Not Available# N. Alias 35561342900 55880849100 57194420119 34969260200 57194406199 22733403000 alternating direction implicit (ADI) method fractional splitting iterative alternating decomposition explicit (IADE) method We consider three level difference replacements of parabolic equations focusing on the heat equation in two space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an alternating direction implicit (ADI) method. Using the well known fact of the parabolic-elliptic correspondence, we shall derive a two stage iterative procedure employing a fractional splitting strategy applied alternately at each intermediate time step to the one dimensional heat equation. As the basis of derivation is the unconditionally stable (4,2) accurate ADI scheme, this method is convergent, computationally stable and highly accurate. � 2006 Inderscience Enterprises Ltd. Final 2023-12-28T08:57:37Z 2023-12-28T08:57:37Z 2006 Article 10.1504/ijspm.2006.009011 2-s2.0-78649831338 https://www.scopus.com/inward/record.uri?eid=2-s2.0-78649831338&doi=10.1504%2fijspm.2006.009011&partnerID=40&md5=1a8d6e40b18f9b48e65e9ed72d105c54 https://irepository.uniten.edu.my/handle/123456789/29773 2 01/02/2023 45 49 Scopus |
| spellingShingle | alternating direction implicit (ADI) method fractional splitting iterative alternating decomposition explicit (IADE) method Sahimi M.S. Mansor N.A. Nor N.M. Nusi N.M. #Not Available# N. Alias A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation |
| title | A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation |
| title_full | A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation |
| title_fullStr | A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation |
| title_full_unstemmed | A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation |
| title_short | A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation |
| title_sort | high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation |
| topic | alternating direction implicit (ADI) method fractional splitting iterative alternating decomposition explicit (IADE) method |
| url_provider | http://dspace.uniten.edu.my/ |