{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T06:00:20Z","timestamp":1767765620885,"version":"3.48.0"},"reference-count":22,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,4]],"date-time":"2026-01-04T00:00:00Z","timestamp":1767484800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper presents two novel hybrid iterative schemes that combine Newton\u2019s method and its variant with the Tuna Swarm Optimization (TSO) algorithm, aimed at solving complex nonlinear equations with enhanced accuracy and efficiency. Newton\u2019s 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.<\/jats:p>","DOI":"10.3390\/a19010040","type":"journal-article","created":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T12:38:56Z","timestamp":1767616736000},"page":"40","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Newton-Based Tuna Swarm Optimization Algorithm for Solving Nonlinear Problems with Application to Differential Equations"],"prefix":"10.3390","volume":"19","author":[{"given":"Aanchal","family":"Chandel","sequence":"first","affiliation":[{"name":"Department of Mathematics, Chandigarh University, Mohali 140413, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1128-3910","authenticated-orcid":false,"given":"Sonia","family":"Bhalla","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Chandigarh University, Mohali 140413, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7462-9173","authenticated-orcid":false,"given":"Alicia","family":"Cordero","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Cno. de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9893-0761","authenticated-orcid":false,"given":"Juan R.","family":"Torregrosa","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Cno. de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1505-8945","authenticated-orcid":false,"given":"Ramandeep","family":"Behl","sequence":"additional","affiliation":[{"name":"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"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/S0952-1976(97)00067-5","article-title":"Solutions to systems of nonlinear equations via a genetic algorithm","volume":"11","author":"Karr","year":"1998","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_2","unstructured":"Epperson, J.F. (2013). An Introduction to Numerical Methods and Analysis, John Wiley & Sons."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0096-3003(93)90137-4","article-title":"A note on the Halley method in Banach spaces","volume":"58","author":"Chen","year":"1993","journal-title":"Appl. Math. Comput."},{"key":"ref_4","unstructured":"Ostrowski, A.M. (1966). 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