Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation
This paper proposes the combination of a preconditioner applied with successive over relaxation (SOR) iterative method for solving a sparse and huge scale linear system (LS) in which its coefficient matrix is a tridiagonal matrix. The purpose for applying the preconditioner is to enhance the converg...
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| Format: | Article |
| Language: | English English |
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Institute of Advanced Engineering and Science (IAES)
2023
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| Online Access: | https://eprints.ums.edu.my/id/eprint/37691/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/37691/2/FULLTEXT.pdf |
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| author | Nur Farah Azira Zainal Jumat Sulaiman Azali Saudi Nur Afza Mat Ali |
| author_facet | Nur Farah Azira Zainal Jumat Sulaiman Azali Saudi Nur Afza Mat Ali |
| author_sort | Nur Farah Azira Zainal |
| collection | UMS |
| description | This paper proposes the combination of a preconditioner applied with successive over relaxation (SOR) iterative method for solving a sparse and huge scale linear system (LS) in which its coefficient matrix is a tridiagonal matrix. The purpose for applying the preconditioner is to enhance the convergence rate of SOR iterative method. Hence, in order to examine the feasibility of the proposed iterative method which is preconditioner SOR (PSOR) iterative method, first we need to derive the approximation equation of one-dimensional (1D) Burgers’ equation through the discretization process in which the second-order implicit finite difference (SIFD) scheme together with semi-approximate (SA) approach have been applied to the proposed problem. Then, the generated LS is modified into preconditioned linear system (PLS) to construct the formulation of PSOR iterative method. Furthemore, to analyze the feasibility of PSOR iterative method compared with other point iterative methods, three examples of 1D Burgers’ equation are considered. In conclusion, the PSOR iterative method is superior than PGS iterative method. The simulation results showed that our proposed iterative method has low iteration numbers and execution time. |
| first_indexed | 2024-03-06T03:26:17Z |
| format | Article |
| id | ums.eprints-37691 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:26:17Z |
| publishDate | 2023 |
| publisher | Institute of Advanced Engineering and Science (IAES) |
| record_format | dspace |
| spelling | ums.eprints-376912023-12-05T04:17:31Z https://eprints.ums.edu.my/id/eprint/37691/ Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation Nur Farah Azira Zainal Jumat Sulaiman Azali Saudi Nur Afza Mat Ali QA299.6-433 Analysis This paper proposes the combination of a preconditioner applied with successive over relaxation (SOR) iterative method for solving a sparse and huge scale linear system (LS) in which its coefficient matrix is a tridiagonal matrix. The purpose for applying the preconditioner is to enhance the convergence rate of SOR iterative method. Hence, in order to examine the feasibility of the proposed iterative method which is preconditioner SOR (PSOR) iterative method, first we need to derive the approximation equation of one-dimensional (1D) Burgers’ equation through the discretization process in which the second-order implicit finite difference (SIFD) scheme together with semi-approximate (SA) approach have been applied to the proposed problem. Then, the generated LS is modified into preconditioned linear system (PLS) to construct the formulation of PSOR iterative method. Furthemore, to analyze the feasibility of PSOR iterative method compared with other point iterative methods, three examples of 1D Burgers’ equation are considered. In conclusion, the PSOR iterative method is superior than PGS iterative method. The simulation results showed that our proposed iterative method has low iteration numbers and execution time. Institute of Advanced Engineering and Science (IAES) 2023-03 Article NonPeerReviewed text en https://eprints.ums.edu.my/id/eprint/37691/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/37691/2/FULLTEXT.pdf Nur Farah Azira Zainal and Jumat Sulaiman and Azali Saudi and Nur Afza Mat Ali (2023) Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation. The Indonesian Journal of Electrical Engineering and Computer Science (IJEECS), 29 (3). pp. 1606-1613. ISSN 2502-4752 http://doi.org/10.11591/ijeecs.v29.i3.pp1606-1613 |
| spellingShingle | QA299.6-433 Analysis Nur Farah Azira Zainal Jumat Sulaiman Azali Saudi Nur Afza Mat Ali Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation |
| title | Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation |
| title_full | Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation |
| title_fullStr | Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation |
| title_full_unstemmed | Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation |
| title_short | Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation |
| title_sort | preconditioned successive over relaxation iterative method via semi approximate approach for burgers equation |
| topic | QA299.6-433 Analysis |
| url | https://eprints.ums.edu.my/id/eprint/37691/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/37691/2/FULLTEXT.pdf |
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