Version 1
: Received: 26 February 2020 / Approved: 27 February 2020 / Online: 27 February 2020 (16:02:39 CET)
How to cite:
Shams, M.; Mir, N.; Rafiq, N. On Efficient Iterative Numerical Methods for Simultaneous Determination of all Roots of Non-Linear Function. Preprints2020, 2020020410. https://doi.org/10.20944/preprints202002.0410.v1
Shams, M.; Mir, N.; Rafiq, N. On Efficient Iterative Numerical Methods for Simultaneous Determination of all Roots of Non-Linear Function. Preprints 2020, 2020020410. https://doi.org/10.20944/preprints202002.0410.v1
Shams, M.; Mir, N.; Rafiq, N. On Efficient Iterative Numerical Methods for Simultaneous Determination of all Roots of Non-Linear Function. Preprints2020, 2020020410. https://doi.org/10.20944/preprints202002.0410.v1
APA Style
Shams, M., Mir, N., & Rafiq, N. (2020). On Efficient Iterative Numerical Methods for Simultaneous Determination of all Roots of Non-Linear Function. Preprints. https://doi.org/10.20944/preprints202002.0410.v1
Chicago/Turabian Style
Shams, M., Nazir Mir and Naila Rafiq. 2020 "On Efficient Iterative Numerical Methods for Simultaneous Determination of all Roots of Non-Linear Function" Preprints. https://doi.org/10.20944/preprints202002.0410.v1
Abstract
We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.
Keywords
Single roots; Distinct roots; Multiple roots; Optimal order; Non-Linear equation; Iterative methods; Simultaneous Methods; Basin of attraction; Computational Efficiency
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.