A new variant of secant technique for simulation of nonlinear equations
Inderjeetinderjeet.7640890021@ipu.ac.in; yadavinderjeet386@gmail.comUniversity School of Basic & Applied Sciences Guru Gobind Singh Indraprastha UniversityDwarka, Delhi, 110078, India0009-0007-7221-6301View full profile → , *Rashmi BhardwajCorresponding authorrashmib@ipu.ac.inNonlinear Dynamics Research Lab University School of Basic & Applied Sciences Guru Gobind Singh Indraprastha UniversityDwarka, Delhi, 110078, India0000-0002-0502-762XView full profile →
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- Received:
- 07 Jan 2025
- Published Online:
- 28 Oct 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2326
- Pages:
- 2867–2876
Abstract
Keywords
Subject Classifications
References
[1] A. M. Ostrowski, Solution of Equations in Euclidean and Banach Space, 3rd ed. New York, NY, USA: Academic Press (1973).
[2] J. F. Traub, Iterative Methods for the Solution of Equations. Englewood Cliffs, NJ, USA: Prentice-Hall (1964).
[3] S. Amat, S. Busquier, and J. M. Gutiérrez, “Geometric constructions of iterative functions to solve nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 157, pp. 197–205 (2003).
[4] V. Kanwar and S. K. Tomar, “Modified families of Newton, Halley and Chebyshev methods,” Applied Mathematics and Computation, vol. 192, pp. 20–26 (2007).
[5] M. Frontini and E. Sormani, “Some variants of Newton’s method with third-order convergence,” Applied Mathematics and Computation, vol. 140, pp. 419–426 (2003).
[6] H. H. H. Homeier, “On Newton-type methods with cubic convergence,” Journal of Computational and Applied Mathematics, vol. 176, pp. 425–432 (2005).
[7] J. Kou, Y. Li, and X. Wang, “Third-order modification of Newton’s method,” Journal of Computational and Applied Mathematics, vol. 205, pp. 1–5 (2007).
[8] A. Y. Özban, “Some new variants of Newton’s method,” Applied Mathematics Letters, vol. 17, pp. 677–682 (2004).
[9] S. Weerakoon and T. G. I. Fernando, “A variant of Newton’s method with accelerated third-order convergence,” Applied Mathematics Letters, vol. 13, pp. 87–93 (2000).
[10] I. K. Argyros, D. Chen, and Q. Qian, “The Jarratt method in Banach space setting,” Journal of Computational and Applied Mathematics, vol. 51, pp. 103–106 (1994).
[11] C. Chun, “Some second-derivative-free variants of Chebyshev-Halley methods,” Applied Mathematics and Computation, vol. 191, pp. 410–414 (2007).
[12] C. Chun, “On the construction of iterative methods with at least cubic convergence,” Applied Mathematics and Computation, vol. 189, pp. 1384–1392 (2007).
[13] V. Kanwar and S. K. Tomar, “Modified families of multi-point iterative methods for solving nonlinear equations,” Numerical Algorithms, vol. 44, pp. 381–389 (2007).
[14] J. Kou, Y. Li, and X. Wang, “A modification of Newton method with third-order convergence,” Applied Mathematics and Computation, vol. 181, pp. 1106–1111 (2006).
[15] L. D. Petković and M. S. Petković, “A note on some recent methods for solving nonlinear equations,” Applied Mathematics and Computation, vol. 185, pp. 368–374 (2007).
[16] F. A. Potra and V. Pták, Non-discrete Induction and Iterative Processes, vol. 103, Research Notes in Mathematics. Boston, MA, USA: Pitman (1984).
[17] J. R. Sharma, “A composite third order Newton-Steffensen method for solving nonlinear equations,” Applied Mathematics and Computation, vol. 169, pp. 242–246 (2005).
[18] R. Thukral, “Introduction to a Newton-type method for solving nonlinear equations,” Applied Mathematics and Computation, vol. 195, pp. 663–668 (2008).
[19] N. Ujević, “An iterative method for solving nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 201, pp. 208–216 (2007).
[20] S. K. Parhia and D. K. Gupta, “A sixth order method for nonlinear equations,” Applied Mathematics and Computation, vol. 203, pp. 50–55 (2008).
[21] A. Rafiq, M. Awais, and F. Zafar, “Modified efficient variant of super-Halley method,” Applied Mathematics and Computation, vol. 189, pp. 2004–2010 (2007).
[22] H. Zhang, L. De-Sheng, and L. Yu-Zhong, “A new method of secant-like for nonlinear equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, pp. 2923–2927 (2009).
[23] R. L. Burden and J. D. Faires, Numerical Analysis, Cengage Learning (2016).
[24] P. Dutta and R. Bhattacharya, “A critical analysis of the secant method for multiple roots,” Journal of Computational and Applied Mathematics, vol. 358, pp. 123–135 (2019).
[25] M. Kheirandish and B. Ebrahimi, “Improving the secant method for nonlinear equations: Convergence analysis and applications,” Applied Numerical Mathematics, vol. 155, pp. 113–128 (2020).
[26] H. H. H. Homeier, “A modified Newton method for root finding with cubic convergence,” Journal of Computational and Applied Mathematics, vol. 157, pp. 227–230 (2003).
[27] A. A. Magreñán, “Different anomalies in a Jarratt family of iterative root-finding methods,” Applied Mathematics and Computation, vol. 233, pp. 29–38 (2014).
[28] S. Amat, S. Busquier, and J. M. Gutiérrez, “Third-order iterative methods with applications to Hammerstein equations: A unified approach,” Journal of Computational and Applied Mathematics, vol. 235, pp. 2936–2943 (2011).
[29] O. Ogbereyivwe and V. Ojo-Orobosa, “Family of optimal two-step fourth order iterative method and its extension for solving nonlinear equations,” Journal of Interdisciplinary Mathematics, vol. 24, no. 5, pp. 1347–1365 (2021). doi: 10.1080/09720502.2021.1884393.
[30] Y. A. Laylani, S. M. Abdullah, and B. A. Hassan, “An innovative secant technique for minima one variable problems,” Journal of Interdisciplinary Mathematics, vol. 28, no. 1, pp. 115–121 (2025). doi: 10.47974/JIM-1805.
[31] Y. Inderjeet and R. Bhardwaj, “A new iterative Newton-Raphson technique for the numerical simulation of nonlinear equations,” Journal of International Science and Technology, vol. 13, p. 1080 (2025).
[32] Y. Inderjeet and R. Bhardwaj, “Newton-Raphson based iterative method for simulating nonlinear equations,” International Research Journal of Multidisciplinary Scope, vol. 6, pp. 857–866 (2025).




