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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...

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Main Authors: Iqbal, Mudassar, Nooraini, Zainuddin, Hanita, Daud, Kanan, Ramani, Rahimah, Jusoh, Ullah, Atta, Khan, Ilyas Kareem
Format: Article
Language:English
Published: Semarak Ilmu Publishing 2024
Subjects:
QA Mathematics
Online Access:http://umpir.ump.edu.my/id/eprint/42188/1/Numerical%20Solution%20of%20Heat%20Equation%20using%20Modified%20Cubic%20B-spline.pdf
http://umpir.ump.edu.my/id/eprint/42188/
https://doi.org/10.37934/arnht.20.1.2335
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spelling my.ump.umpir.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
institution Universiti Malaysia Pahang Al-Sultan Abdullah
building UMPSA Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Pahang Al-Sultan Abdullah
content_source UMPSA Institutional Repository
url_provider http://umpir.ump.edu.my/
language English
topic QA Mathematics
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
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.
format Article
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
title 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_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_sort numerical solution of heat equation using modified cubic b-spline collocation method
publisher Semarak Ilmu Publishing
publishDate 2024
url http://umpir.ump.edu.my/id/eprint/42188/1/Numerical%20Solution%20of%20Heat%20Equation%20using%20Modified%20Cubic%20B-spline.pdf
http://umpir.ump.edu.my/id/eprint/42188/
https://doi.org/10.37934/arnht.20.1.2335
_version_ 1822924570233929728
score 13.239859

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