On numerical schemes for determination of all roots simultaneously of non-linear equation

  • Nazir Ahmad Mir Department of Mathematics and Statistics, Riphah International University, Islamabad Pakistan Department of Mathematics, National University of Modern Languages, Islamabad Pakistan
  • Maria Anwar Department of Mathematics and Statistics, Riphah International University, Islamabad Pakistan
  • Mudassir Shams Department of Mathematics and Statistics, Riphah International University, Islamabad Pakistan
  • Naila Rafiq Department of Mathematics, National University of Modern Languages, Islamabad Pakistan
  • Saima Akram Center for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan Pakistan

Abstract

In this article, we first construct family of two-step optimal fourth order iterative methods for finding single root of non-linear equation. We then extend these methods for determining all the distinct as well as multiple roots of single variable non-linear equation simultaneously. Convergence analysis is presented for both the cases to show that the optimal order of convergence is 4 in case of single root finding method and 6 for simultaneous determination of all distinct as well as multiple roots of a non-linear equation. The computational cost, basins of attraction, computational efficiency, log of residual fall and numerical test functions validate that the newly constructed methods are more efficient as compared to the existing methods in the literature.

Published
Apr 1, 2022
How to Cite
MIR, Nazir Ahmad et al. On numerical schemes for determination of all roots simultaneously of non-linear equation. Mehran University Research Journal of Engineering and Technology, [S.l.], v. 41, n. 2, p. 208-218, apr. 2022. ISSN 2413-7219. Available at: <https://publications.muet.edu.pk/index.php/muetrj/article/view/2454>. Date accessed: 17 may 2022. doi: http://dx.doi.org/10.22581/muet1982.2202.20.
Section
Articles
This is an open Access Article published by Mehran University of Engineering and Technolgy, Jamshoro under CCBY 4.0 International License