Numerical solution of heat equation using modified cubic B-spline collocation method
In this paper, a collocation method is presented based on the Modified Cubic B-spline Method (MCBSM) for the numerical solution of the heat equation. The PDE is fully discretized by using the Modified Cubic B-spline basis collocation for spatial discretization and the finite difference method is use...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Semarak Ilmu Publishing
2024
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| Online Access: | http://umpir.ump.edu.my/id/eprint/42188/ http://umpir.ump.edu.my/id/eprint/42188/1/Numerical%20Solution%20of%20Heat%20Equation%20using%20Modified%20Cubic%20B-spline.pdf |
| _version_ | 1848826544038871040 |
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| author | Iqbal, Mudassar Nooraini, Zainuddin Hanita, Daud Kanan, Ramani Rahimah, Jusoh Ullah, Atta Khan, Ilyas Kareem |
| author_facet | Iqbal, Mudassar Nooraini, Zainuddin Hanita, Daud Kanan, Ramani Rahimah, Jusoh Ullah, Atta Khan, Ilyas Kareem |
| author_sort | Iqbal, Mudassar |
| building | UMP Institutional Repository |
| collection | Online Access |
| description | In this paper, a collocation method is presented based on the Modified Cubic B-spline Method (MCBSM) for the numerical solution of the heat equation. The PDE is fully discretized by using the Modified Cubic B-spline basis collocation for spatial discretization and the finite difference method is used for the time discretization. A numerical example from PDE is used to evaluate the accuracy of the proposed method. The numerical results are evaluated in comparison to the exact solutions. The findings consistently indicate that the suggested technique provides good error estimates. We also discovered that our proposed method was unconditionally stable. Hence, based on the results and the efficiency of the method, the method is suitable for solving heat equation. |
| first_indexed | 2025-11-15T03:46:30Z |
| format | Article |
| id | ump-42188 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T03:46:30Z |
| publishDate | 2024 |
| publisher | Semarak Ilmu Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-421882024-08-06T08:13:31Z http://umpir.ump.edu.my/id/eprint/42188/ Numerical solution of heat equation using modified cubic B-spline collocation method Iqbal, Mudassar Nooraini, Zainuddin Hanita, Daud Kanan, Ramani Rahimah, Jusoh Ullah, Atta Khan, Ilyas Kareem QA Mathematics In this paper, a collocation method is presented based on the Modified Cubic B-spline Method (MCBSM) for the numerical solution of the heat equation. The PDE is fully discretized by using the Modified Cubic B-spline basis collocation for spatial discretization and the finite difference method is used for the time discretization. A numerical example from PDE is used to evaluate the accuracy of the proposed method. The numerical results are evaluated in comparison to the exact solutions. The findings consistently indicate that the suggested technique provides good error estimates. We also discovered that our proposed method was unconditionally stable. Hence, based on the results and the efficiency of the method, the method is suitable for solving heat equation. Semarak Ilmu Publishing 2024 Article PeerReviewed pdf en cc_by_nc_4 http://umpir.ump.edu.my/id/eprint/42188/1/Numerical%20Solution%20of%20Heat%20Equation%20using%20Modified%20Cubic%20B-spline.pdf Iqbal, Mudassar and Nooraini, Zainuddin and Hanita, Daud and Kanan, Ramani and Rahimah, Jusoh and Ullah, Atta and Khan, Ilyas Kareem (2024) Numerical solution of heat equation using modified cubic B-spline collocation method. Journal of Advanced Research in Numerical Heat Transfer, 20 (1). pp. 23-35. ISSN 2735-0142. (Published) https://doi.org/10.37934/arnht.20.1.2335 10.37934/arnht.20.1.2335 |
| spellingShingle | QA Mathematics Iqbal, Mudassar Nooraini, Zainuddin Hanita, Daud Kanan, Ramani Rahimah, Jusoh Ullah, Atta Khan, Ilyas Kareem Numerical solution of heat equation using modified cubic B-spline collocation method |
| title | Numerical solution of heat equation using modified cubic B-spline collocation method |
| title_full | Numerical solution of heat equation using modified cubic B-spline collocation method |
| title_fullStr | Numerical solution of heat equation using modified cubic B-spline collocation method |
| title_full_unstemmed | Numerical solution of heat equation using modified cubic B-spline collocation method |
| title_short | Numerical solution of heat equation using modified cubic B-spline collocation method |
| title_sort | numerical solution of heat equation using modified cubic b-spline collocation method |
| topic | QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/42188/ http://umpir.ump.edu.my/id/eprint/42188/ http://umpir.ump.edu.my/id/eprint/42188/ http://umpir.ump.edu.my/id/eprint/42188/1/Numerical%20Solution%20of%20Heat%20Equation%20using%20Modified%20Cubic%20B-spline.pdf |