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Algorithms
Volume 19
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10.3390/a19010040
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

A Newton-Based Tuna Swarm Optimization Algorithm for Solving Nonlinear Problems with Application to Differential Equations

by
Aanchal Chandel
1,
Sonia Bhalla
1,
Alicia Cordero
2,*,
Juan R. Torregrosa
2 and
Ramandeep Behl
3
1
Department of Mathematics, Chandigarh University, Mohali 140413, India
2
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Cno. de Vera s/n, 46022 Valencia, Spain
3
Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
*
Author to whom correspondence should be addressed.
Algorithms 2026, 19(1), 40; https://doi.org/10.3390/a19010040
Submission received: 9 December 2025 / Revised: 29 December 2025 / Accepted: 30 December 2025 / Published: 4 January 2026
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (4th Edition))
Versions Notes

Abstract

This paper presents two novel hybrid iterative schemes that combine Newton’s method and its variant with the Tuna Swarm Optimization (TSO) algorithm, aimed at solving complex nonlinear equations with enhanced accuracy and efficiency. Newton’s method is renowned for its rapid convergence in root-finding problems, and it is integrated with TSO, a recent swarm intelligence algorithm that surpasses the complex behavior of tuna fish in order to optimize the search for superior solutions. These hybrid methods are reliable and efficient for solving challenging mathematical and applied science problems. Several numerical experiments and applications involving ordinary differential equations have been carried out to demonstrate the superiority of the proposed hybrid methods in terms of convergence rate, accuracy, and robustness compared to traditional optimization and iterative methods. The stability and efficiency of the proposed methods have also been verified. The results indicate that the hybrid approaches outperform traditional methods, making them a promising tool for solving a wide range of mathematical and engineering problems.
Keywords: nonlinear systems; Newton’s method; meta-heuristic techniques; tuna swarm optimization nonlinear systems; Newton’s method; meta-heuristic techniques; tuna swarm optimization

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MDPI and ACS Style

Chandel, A.; Bhalla, S.; Cordero, A.; Torregrosa, J.R.; Behl, R. A Newton-Based Tuna Swarm Optimization Algorithm for Solving Nonlinear Problems with Application to Differential Equations. Algorithms 2026, 19, 40. https://doi.org/10.3390/a19010040

AMA Style

Chandel A, Bhalla S, Cordero A, Torregrosa JR, Behl R. A Newton-Based Tuna Swarm Optimization Algorithm for Solving Nonlinear Problems with Application to Differential Equations. Algorithms. 2026; 19(1):40. https://doi.org/10.3390/a19010040

Chicago/Turabian Style

Chandel, Aanchal, Sonia Bhalla, Alicia Cordero, Juan R. Torregrosa, and Ramandeep Behl. 2026. "A Newton-Based Tuna Swarm Optimization Algorithm for Solving Nonlinear Problems with Application to Differential Equations" Algorithms 19, no. 1: 40. https://doi.org/10.3390/a19010040

APA Style

Chandel, A., Bhalla, S., Cordero, A., Torregrosa, J. R., & Behl, R. (2026). A Newton-Based Tuna Swarm Optimization Algorithm for Solving Nonlinear Problems with Application to Differential Equations. Algorithms, 19(1), 40. https://doi.org/10.3390/a19010040

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