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  • Date of Publication : 2023-06-26 Article Type : Research Article

    • Numerical Solution of the Heat Equation by Cubic B-spline Collocation Method

    Hoshman Q. Hamad ¹* and Younis A. Sabawi ¹ ² 

     Affiliation

    ¹ Department of Mathematics, Faculty of Science and Health, Koya University, Koya-IRAQ
    ² Department of Mathematics Education, Faculty of Education, Tishk International University, Erbil-IRAQ
    * Correspodning Author 


    ORCID :

    Hoshman Q. Hamad: https://orcid.org/0009-0004-5080-2420, Younis A. Sabawi: https://orcid.org/0000-0002-9807-8409


    DOI :

    https://doi.org/10.23918/eajse.v9i2p20


    Article History

    Received: 2023-01-05

    Revised: 2023-05-04

    Accepted: 2023-06-21
    Abstract

    This work proposes a numerical scheme for heat parabolic problem by implementing a collocation method with a cubic B-spline for a uniform mesh. The key idea of this method is to apply forward finite difference and  Crank–Nicolson methods  for time and space integration, respectively. The stability of the presented scheme is proved through the Von-Neumann technique. It is shown that it is unconditionally stable. The accuracy of the suggested scheme is computed through the  L_2  and L_∞-norms. Numerical experiments are also given and show that it is compatible with the exact solutions.

    Keywords :

    Collocation Methods; Cubic B-Spline Functions; Heat Equation


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    @article{hamad,hoshmanqandsabawi,younisa2023,
 author = {Hamad,  Hoshman Q and Sabawi, Younis A},
 title = {Numerical Solution of the Heat Equation by Cubic B-spline Collocation Method},
 journal = {Eurasian J. Sci. Eng},
 volume = {9},
 number = {2},
 pages = {252-261},
 year = {2023}
}
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    Hamad, H. Q., & Hussain, Y. A. (2023). Numerical Solution of the Heat Equation by Cubic B-spline Collocation Method. Eurasian J. Sci. Eng, 9(2),252-261.

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    Hamad, HQ, and Hussain, YA. "Numerical Solution of the Heat Equation by Cubic B-spline Collocation Method." Eurasian J. Sci. Eng, 9.2, (2023), pp.252-261.

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    Hamad, H.Q. and Hussain, Y.A., (2023) "Numerical Solution of the Heat Equation by Cubic B-spline Collocation Method", Eurasian J. Sci. Eng, 9(2), pp.252-261.

    Copy

    Hamad HQ, Sabawi YA. Numerical Solution of the Heat Equation by Cubic B-spline Collocation Method. Eurasian J. Sci. Eng. 2023; 9(2):252-261.

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  • Numerical Solution of the Heat Equation by Cubic B-spline Collocation Method