Numerical Solution of Heat Equation using Modified Cubic B-spline Collocation Method

Authors

  • Mudassar Iqbal Department of Mathematical Sciences, Faculty of Basic Sciences, Balochistan University of Information Technology, Engineering and Management Sciences (BUITEMS), Quetta, Pakistan
  • Nooraini Zainuddin Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Bandar Seri Iskandar, Malaysia.
  • Hanita Daud Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Bandar Seri Iskandar, Malaysia.
  • Ramani Kanan Department of Electrical and Electronics Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia
  • Rahimah Jusoh Centre for Mathematical Sciences, Universiti Malaysia Pahang, 26300 Gambang, Kuantan, Pahang, Malaysia
  • Atta Ullah Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Bandar Seri Iskandar, Malaysia
  • Ilyas Kareem Khan Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Bandar Seri Iskandar, Malaysia

DOI:

https://doi.org/10.37934/arnht.20.1.2335

Keywords:

Modified Cubic B-Spline Method, Collocation Method, Partial Differential Equations, Heat Equation, Error Analysis, Numerical Solutions

Abstract

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.

Author Biographies

Mudassar Iqbal, Department of Mathematical Sciences, Faculty of Basic Sciences, Balochistan University of Information Technology, Engineering and Management Sciences (BUITEMS), Quetta, Pakistan

mudassar.iqbal@buitms.edu.pk

Nooraini Zainuddin, Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Bandar Seri Iskandar, Malaysia.

aini_zainuddin@utp.edu.my

Hanita Daud, Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Bandar Seri Iskandar, Malaysia.

hanita_daud@utp.edu.my

Ramani Kanan, Department of Electrical and Electronics Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia

ramani.kannan@utp.edu.my

Rahimah Jusoh, Centre for Mathematical Sciences, Universiti Malaysia Pahang, 26300 Gambang, Kuantan, Pahang, Malaysia

rahimahj@ump.edu.my

Atta Ullah, Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Bandar Seri Iskandar, Malaysia

atta_22000639@utp.edu.my

Ilyas Kareem Khan, Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Bandar Seri Iskandar, Malaysia

iliyas_22008363@utp.edu.my

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Published

2024-06-02

How to Cite

Mudassar Iqbal, Nooraini Zainuddin, Hanita Daud, Ramani Kanan, Rahimah Jusoh, Atta Ullah, & Ilyas Kareem Khan. (2024). Numerical Solution of Heat Equation using Modified Cubic B-spline Collocation Method. Journal of Advanced Research in Numerical Heat Transfer, 20(1), 23–35. https://doi.org/10.37934/arnht.20.1.2335

Issue

Vol. 20 No. 1: May (2024)

Section

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