Page 142 - IJOCTA-15-3
P. 142
Srinivasarao Thota et al. / IJOCTA, Vol.15, No.3, pp.503-516 (2025)
Conflict of interest 10. Thota S, Awad MM, Shanmugasundaram P. A
derivative-free root-finding algorithm using expo-
The authors declare that they have no competing
nential method and its implementation. BMC Res
interests.
Notes. 2023;16:276.
https://doi.org/10.1186/s13104-023-06554-1
Author contributions 11. Thota S, Gemechu T, Ayoade AA. On new hybrid
root-finding algorithms for solving transcendental
Conceptualization: Srinivasarao Thota
equations using exponential and halley’s methods.
Formal analysis: Amir Naseem, Thumati Gopi, Ural Math J. 2023; 9(1):176-186.
Kashireddy Sai Nandan Reddy, Padarthi Sai http://dx.doi.org/10.15826/umj.2023.1.016
Kousik 12. Thota S, Gemechu T, Shanmugasundaram P.
Investigation: Thulasi Bikku, Amir Naseem New algorithms for computing non-linear equa-
Methodology: Srinivasarao Thota, Amir Naseem tions using exponential series. Palestine J Math.
Writing – original draft: Srinivasarao Thota 2021; 10(1): 128-134.
Writing – review & editing: Thulasi Bikku, Shan- 13. Thota S. A new root-finding algorithm using ex-
mugasundaram Palanisamy ponential series. Ural Math J. 2022;5(1):83-90.
https://doi.org/10.15826/umj.2019.1.008
14. Thota S. A New Hybrid Halley-False Position
Availability of data
type Root Finding Algorithm to Solve Transcen-
The datasets generated and analyzed during the dental Equations. Istanbul International Modern
current study are presented in this manuscript. Scientific Research Congress-III, 06-08 May 2022,
Istanbul Gedik University, Istanbul, Turkey.
15. Chen D, Argyros IK, Qian QS. A note on the Hal-
References
ley method in Banach spaces. Appl Math Comput.
1. Traub JF. Iterative Methods for the Solution of 1983;58:215-224.
Equations, vol. 312. Providence, RI, USA: Amer- 16. Noor MA, Khan WA, Hussain A. A new mod-
ican Mathematical Society; 1982. ified Halley method without second derivatives
2. Rafiullah M. A fifth-order iterative method for for nonlinear equation. Appl Math Comput.
solving nonlinear equations. Numer Anal Appl. 2007;189:1268-1273.
2011; 4: 239-243. https://doi.org/10.1016/j.amc.2006.12.011
https://doi.org/10.1134/S1995423911030062 17. ‘Cordero A, Hueso JL, Mart´ınez E, Torregrosa
3. Ganji DD. The application of He’s homotopy per- JR. A modified Newton–Jarratt’s composition.
turbation method to nonlinear equations arising Numer Algorithms. 2010; 55:87–99.
in heat transfer. Phys Lett A. 2006;355:337-341. https://doi.org/10.1007/s11075-009-9359-z
https://doi.org/10.1016/j.physleta.2006.02.056 18. Thota S, Ayoade AA. A new numerical algo-
4. Thota S, Shanmugasundaram P. On new sixth rithm to compute a root of non-linear equations
and seventh order iterative methods for solving using exponential method. interplay of fractals
non-linear equations using homotopy perturba- and complexity in mathematical modelling and
tion technique. BMC Res Notes. 2022;15:267. physical patterns. In: ISMAFDS 2023. Cham:
https://doi.org/10.1186/s13104-022-06154-5 Springer; 2025.
5. Abbasbandy S. Improving Newton–Raphson https://doi.org/10.1007/978-3-031-58641-5 2 8
method for nonlinear equations by modified Ado- 19. Noor MA, Noor KI, Al-Said E, Waseem M. Some
mian decomposition method. Appl Math Comput. new iterative methods for nonlinear equations.
2003; 145:887-893. Math Probl Eng . 2010; 198943.
https://doi.org/10.1016/S0096-3003(03)00282-0 https://doi.org/10.1155/2010/198943
6. He JH, Wu XH. Variational iteration method: 20. Noor MA, Noor KI. Three-step iterative methods
new development and applications. Comput Math for nonlinear equations. Appl Math Comput. 2006;
Appl 2007;54:881-894. 183:322-327.
https://doi.org/10.1016/j.camwa.2006.12.083 https://doi.org/10.1016/j.amc.2006.05.055
7. Tari H, Ganji DD, Babazadeh H. The application 21. Shah FA, Noor MA, Waseem M. Some second-
of He’s variational iteration method to nonlinear derivative-free sixth-order convergent iterative
equations arising in heat transfer. Phys Lett A. methods for non-linear equations. Maejo Int J Sci
2007;363:213-217. Technol. 2016; 10(01):79-87.
https://doi.org/10.1016/j.physleta.2006.11.005 https://doi.org/10.14456/mijst.2016.7
8. Noor MA, Waseem M. Some iterative methods for 22. Abro HA, Shaikh MM. A new time-efficient and
solving a system of nonlinear equations. Comput convergent nonlinear solver. Appl Math Comput.
Math Appl. 2009;57:101-106. 2019; 355:516-536.
https://doi.org/10.1016/j.camwa.2008.10.067 https://doi.org/10.1016/j.amc.2019.03.012
9. Zafar F, Mir NA. A generalized family of 23. Torregrosa JR, Argyros IK, Chun C, Cordero
quadrature based iterative methods. Gen Math. A, Soleymani F. Iterative methods for nonlinear
2010;18:43-51. equations or systems and their applications 2014.
514

