Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation
We consider three-level difference replacements of parabolic equations focussing on the heat equation in two- space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an ADI method. Using the well-known fact of the parabolic-elliptic correspondence, we shall deri...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
2003
|
| Subjects: | |
| Online Access: | http://eprints.utm.my/6506/1/v26n1p8.pdf |
| _version_ | 1796854084851990528 |
|---|---|
| author | Sahimi, M. S. Alias, N. Mansor, N. A. Nor, N. M. |
| author_facet | Sahimi, M. S. Alias, N. Mansor, N. A. Nor, N. M. |
| author_sort | Sahimi, M. S. |
| collection | ePrints |
| description | We consider three-level difference replacements of parabolic equations focussing on the heat equation in two- space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an 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. |
| first_indexed | 2024-03-05T18:09:07Z |
| format | Article |
| id | utm.eprints-6506 |
| institution | Universiti Teknologi Malaysia - ePrints |
| language | English |
| last_indexed | 2024-03-05T18:09:07Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | utm.eprints-65062011-05-10T08:58:45Z http://eprints.utm.my/6506/ Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation Sahimi, M. S. Alias, N. Mansor, N. A. Nor, N. M. QA Mathematics We consider three-level difference replacements of parabolic equations focussing on the heat equation in two- space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an 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. 2003 Article PeerReviewed application/pdf en http://eprints.utm.my/6506/1/v26n1p8.pdf Sahimi, M. S. and Alias, N. and Mansor, N. A. and Nor, N. M. (2003) Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation. Bulletin of the Malaysian Mathematical Sciences Society . pp. 79-85. |
| spellingShingle | QA Mathematics Sahimi, M. S. Alias, N. Mansor, N. A. Nor, N. M. Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation |
| title | Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation |
| title_full | Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation |
| title_fullStr | Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation |
| title_full_unstemmed | Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation |
| title_short | Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation |
| title_sort | parabolic elliptic correspondence of a three level finite difference approximation to the heat equation |
| topic | QA Mathematics |
| url | http://eprints.utm.my/6506/1/v26n1p8.pdf |
| work_keys_str_mv | AT sahimims parabolicellipticcorrespondenceofathreelevelfinitedifferenceapproximationtotheheatequation AT aliasn parabolicellipticcorrespondenceofathreelevelfinitedifferenceapproximationtotheheatequation AT mansorna parabolicellipticcorrespondenceofathreelevelfinitedifferenceapproximationtotheheatequation AT nornm parabolicellipticcorrespondenceofathreelevelfinitedifferenceapproximationtotheheatequation |