Volume 11, Issue 1 (January 2024), Pages: 201-206

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 Technical Note

Legendre operational differential matrix for solving ordinary differential equations

 Author(s): 

 Zainab I. Mousa ^1, *, Mazin H. Suhhiem ²

 Affiliation(s):

 ¹Department of Mathematics, University of Kufa, Kufa, Iraq
 ²Department of Mathematics, University of Sumer, Al-Rifai, Iraq

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-7766-5698

 Digital Object Identifier (DOI)

 https://doi.org/10.21833/ijaas.2024.01.024

 Abstract

In this paper, we used the Legendre operational differential matrix method based on the Tau method to find the approximate analytical solutions to the initial value problems and boundary value problems of ordinary differential equations. This method allows the solution of the ordinary differential equation to be computed in the form of an infinite series in which the components can be easily calculated. We introduced a comparison between the approximate solution that we computed and the exact solution of the selected problem, as we found the absolute error. According to the numerical results, the series of solutions we found are accurate and very close to the exact analytical solutions.

 © 2024 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords

 Legendre operational differential matrix, Tau method, Ordinary differential equations, Approximate analytical solutions, Absolute error comparison

 Article history

 Received 24 August 2023, Received in revised form 14 January 2024, Accepted 15 January 2024

 Acknowledgment 

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Mousa ZI and Suhhiem MH (2024). Legendre operational differential matrix for solving ordinary differential equations. International Journal of Advanced and Applied Sciences, 11(1): 201-206

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 Tables

 Table 1 Table 2 Table 3

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