Extended accelerated overrelaxation iteration techniques in solving heat distribution problems
Several stationary iteration techniques for numerical solutions to special systems of linear equation systems of the form 𝒜𝑢 = 𝑏 have been studied in an attempt to improve their convergence, suitability, and strength. Among such techniques is the Extended Accelerated Overrelaxation (EAOR) iterativ...
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| Format: | Article |
| Language: | English |
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Prince of Songkla University
2022-10-01
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| Series: | Songklanakarin Journal of Science and Technology (SJST) |
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| Online Access: | https://sjst.psu.ac.th/journal/44-5/10.pdf |
| _version_ | 1827960382873927680 |
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| author | Khadeejah James Audu |
| author_facet | Khadeejah James Audu |
| author_sort | Khadeejah James Audu |
| collection | DOAJ |
| description | Several stationary iteration techniques for numerical solutions to special systems of linear equation systems of the form
𝒜𝑢 = 𝑏 have been studied in an attempt to improve their convergence, suitability, and strength. Among such techniques is the
Extended Accelerated Overrelaxation (EAOR) iterative scheme. In this paper, we studied the basics of the EAOR methods and
applied them to compute the solution of a real-life problem, resolving the heat equation when a steady temperature is applied to a
metal plate. We show how the real-life problem can be modeled into a partial differential equation, followed by discretization
through the use of finite differences, and finally generating a largely sparse system of algebraic linear equations, from which the
unknowns are to be solved. The techniques were compared with the Refinement of Accelerated Overrelaxation (RAOR) iterative
scheme. The outcome of the numerical tests proves the effectiveness of the EAOR schemes for such problems.
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| first_indexed | 2024-04-09T16:07:36Z |
| format | Article |
| id | doaj.art-8874c75a3e76474b8845f0f4ba598fc4 |
| institution | Directory Open Access Journal |
| issn | 0125-3395 |
| language | English |
| last_indexed | 2024-04-09T16:07:36Z |
| publishDate | 2022-10-01 |
| publisher | Prince of Songkla University |
| record_format | Article |
| series | Songklanakarin Journal of Science and Technology (SJST) |
| spelling | doaj.art-8874c75a3e76474b8845f0f4ba598fc42023-04-25T03:54:36ZengPrince of Songkla UniversitySongklanakarin Journal of Science and Technology (SJST)0125-33952022-10-014451232123710.14456/sjst-psu.2022.160Extended accelerated overrelaxation iteration techniques in solving heat distribution problemsKhadeejah James Audu0Department of Mathematics, Federal University of Technology, Minna, NigeriaSeveral stationary iteration techniques for numerical solutions to special systems of linear equation systems of the form 𝒜𝑢 = 𝑏 have been studied in an attempt to improve their convergence, suitability, and strength. Among such techniques is the Extended Accelerated Overrelaxation (EAOR) iterative scheme. In this paper, we studied the basics of the EAOR methods and applied them to compute the solution of a real-life problem, resolving the heat equation when a steady temperature is applied to a metal plate. We show how the real-life problem can be modeled into a partial differential equation, followed by discretization through the use of finite differences, and finally generating a largely sparse system of algebraic linear equations, from which the unknowns are to be solved. The techniques were compared with the Refinement of Accelerated Overrelaxation (RAOR) iterative scheme. The outcome of the numerical tests proves the effectiveness of the EAOR schemes for such problems. https://sjst.psu.ac.th/journal/44-5/10.pdfextended accelerated overrelaxation methoddiscretizationspectral radiusheat transferlarge linear equation system |
| spellingShingle | Khadeejah James Audu Extended accelerated overrelaxation iteration techniques in solving heat distribution problems Songklanakarin Journal of Science and Technology (SJST) extended accelerated overrelaxation method discretization spectral radius heat transfer large linear equation system |
| title | Extended accelerated overrelaxation iteration techniques in solving heat distribution problems |
| title_full | Extended accelerated overrelaxation iteration techniques in solving heat distribution problems |
| title_fullStr | Extended accelerated overrelaxation iteration techniques in solving heat distribution problems |
| title_full_unstemmed | Extended accelerated overrelaxation iteration techniques in solving heat distribution problems |
| title_short | Extended accelerated overrelaxation iteration techniques in solving heat distribution problems |
| title_sort | extended accelerated overrelaxation iteration techniques in solving heat distribution problems |
| topic | extended accelerated overrelaxation method discretization spectral radius heat transfer large linear equation system |
| url | https://sjst.psu.ac.th/journal/44-5/10.pdf |
| work_keys_str_mv | AT khadeejahjamesaudu extendedacceleratedoverrelaxationiterationtechniquesinsolvingheatdistributionproblems |