Two-level compact implicit schemes for three-dimensional parabolic problems.
We derive a class of two-level high-order implicit finite difference schemes for solving three-dimensional parabolic problems with mixed derivatives. The schemes are fourth-order accurate in space and second- or lower-order accurate in time depending on the choice of a weighted average parameter μ....
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| Format: | Article |
| Language: | English English |
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Elsevier
2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/17503/ http://psasir.upm.edu.my/id/eprint/17503/1/Two.pdf |
| _version_ | 1848843259384692736 |
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| author | Karaa, Samir Othman, Mohamed |
| author_facet | Karaa, Samir Othman, Mohamed |
| author_sort | Karaa, Samir |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We derive a class of two-level high-order implicit finite difference schemes for solving three-dimensional parabolic problems with mixed derivatives. The schemes are fourth-order accurate in space and second- or lower-order accurate in time depending on the choice of a weighted average parameter μ. Numerical results with μ=0.5 are presented to confirm the high accuracy of the derived scheme and to compare it with the standard second-order central difference scheme. It is shown that the improvement in accuracy does not come at a higher cost of computation and storage since it is possible to choose the grid parameters so that the present scheme requires less work and memory and gives more accuracy than the standard central difference scheme. |
| first_indexed | 2025-11-15T08:12:11Z |
| format | Article |
| id | upm-17503 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T08:12:11Z |
| publishDate | 2009 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-175032015-09-28T03:26:27Z http://psasir.upm.edu.my/id/eprint/17503/ Two-level compact implicit schemes for three-dimensional parabolic problems. Karaa, Samir Othman, Mohamed We derive a class of two-level high-order implicit finite difference schemes for solving three-dimensional parabolic problems with mixed derivatives. The schemes are fourth-order accurate in space and second- or lower-order accurate in time depending on the choice of a weighted average parameter μ. Numerical results with μ=0.5 are presented to confirm the high accuracy of the derived scheme and to compare it with the standard second-order central difference scheme. It is shown that the improvement in accuracy does not come at a higher cost of computation and storage since it is possible to choose the grid parameters so that the present scheme requires less work and memory and gives more accuracy than the standard central difference scheme. Elsevier 2009 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/17503/1/Two.pdf Karaa, Samir and Othman, Mohamed (2009) Two-level compact implicit schemes for three-dimensional parabolic problems. Computers and Mathematics with Applications, 58 (1). pp. 257-263. ISSN 0898-1221 http://www.elsevier.com Differential equations, Parabolic. Differential equations - Problems, exercises, etc. Dimensional analysis. http://dx.doi.org/10.1016/j.camwa.2009.02.036 English |
| spellingShingle | Differential equations, Parabolic. Differential equations - Problems, exercises, etc. Dimensional analysis. Karaa, Samir Othman, Mohamed Two-level compact implicit schemes for three-dimensional parabolic problems. |
| title | Two-level compact implicit schemes for three-dimensional parabolic problems. |
| title_full | Two-level compact implicit schemes for three-dimensional parabolic problems. |
| title_fullStr | Two-level compact implicit schemes for three-dimensional parabolic problems. |
| title_full_unstemmed | Two-level compact implicit schemes for three-dimensional parabolic problems. |
| title_short | Two-level compact implicit schemes for three-dimensional parabolic problems. |
| title_sort | two-level compact implicit schemes for three-dimensional parabolic problems. |
| topic | Differential equations, Parabolic. Differential equations - Problems, exercises, etc. Dimensional analysis. |
| url | http://psasir.upm.edu.my/id/eprint/17503/ http://psasir.upm.edu.my/id/eprint/17503/ http://psasir.upm.edu.my/id/eprint/17503/ http://psasir.upm.edu.my/id/eprint/17503/1/Two.pdf |