Abstract:
The objective of this paper is to propose two new hybrid root finding algorithms for solving transcendental equations. The proposed algorithms are based on the well-known root finding methods namely the Halley's method, regula-falsi method and exponential method. We show using numerical examples that the proposed algorithms converge faster than other related methods. The first hybrid algorithm consists of regula-falsi method and exponential method (RF-EXP). In the second hybrid algorithm, we use regula-falsi method and Halley's method (RF-Halley). Several numerical examples are presented to illustrate the proposed algorithms, and comparison of these algorithms with other existing methods are presented to show the efficiency and accuracy. The implementation of the proposed algorithms is presented in
Microsoft Excel (MS Excel) and the mathematical software tool Maple.
\Bibitem{ThoGemAyo23}
\by Srinivasarao~Thota, Tekle~Gemechu, Abayomi~Ayotunde~Ayoade
\paper On new hybrid root-finding algorithms for solving transcendental equations using exponential and Halley's methods
\jour Ural Math. J.
\yr 2023
\vol 9
\issue 1
\pages 176--186
\mathnet{http://mi.mathnet.ru/umj198}
\crossref{https://doi.org/10.15826/umj.2023.1.016}
\elib{https://elibrary.ru/item.asp?id=54265316}
\edn{https://elibrary.ru/BGBNJN}
Linking options:
https://www.mathnet.ru/eng/umj198
https://www.mathnet.ru/eng/umj/v9/i1/p176
This publication is cited in the following 2 articles:
Srinivasarao Thota, Abayomi Ayotunde Ayoade, Interplay of Fractals and Complexity in Mathematical Modelling and Physical Patterns, 2025, 415
Srinivasarao Thota, Mohamed M. Awad, P. Shanmugasundaram, Laxmi Rathour, “A derivative-free root-finding algorithm using exponential method and its implementation”, BMC Res Notes, 16:1 (2023)
Citation in format AMSBIB
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