{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,25]],"date-time":"2025-12-25T05:16:37Z","timestamp":1766639797924,"version":"3.48.0"},"reference-count":25,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T00:00:00Z","timestamp":1766448000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009392","name":"Prince Sattam bin Abdulaziz University","doi-asserted-by":"crossref","award":["PSAU\/2025\/01\/33287"],"award-info":[{"award-number":["PSAU\/2025\/01\/33287"]}],"id":[{"id":"10.13039\/100009392","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Non-linear systems of equations play a fundamental role in various engineering and data science models, where accurate solutions are essential for both theoretical research and practical applications. However, solving such systems is highly challenging due to their inherent non-linearity and computational complexity. This study proposes a novel hybrid iterative method with fourth-order convergence. The foundation of the proposed scheme combines the Walrus Optimization Algorithm and a fourth-order iterative technique. The objective of this hybrid approach is to enhance global search capability, reduce the likelihood of convergence to local optima, accelerate convergence, and improve solution accuracy in solving non-linear problems. The effectiveness of the proposed method is checked on standard benchmark problems and two real-world case studies, hydrocarbon combustion and electronic circuit design, and one non-linear boundary value problem. In addition, a comparative analysis is conducted with several well-established optimization algorithms, based on the optimal solution, average fitness value, and convergence rate. Furthermore, the proposed scheme effectively addresses key limitations of traditional iterative techniques, such as sensitivity to initial point selection, divergence issues, and premature convergence. These findings demonstrate that the proposed hybrid method is a robust and efficient approach for solving non-linear problems.<\/jats:p>","DOI":"10.3390\/axioms15010006","type":"journal-article","created":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T14:27:47Z","timestamp":1766500067000},"page":"6","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Hybrid Walrus Optimization-Based Fourth-Order Method for Solving Non-Linear Problems"],"prefix":"10.3390","volume":"15","author":[{"given":"Aanchal","family":"Chandel","sequence":"first","affiliation":[{"name":"Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2869-4334","authenticated-orcid":false,"given":"Eulalia","family":"Mart\u00ednez","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e9cnica de Val\u00e9ncia, 46002 Val\u00e9ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sonia","family":"Bhalla","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-1777-9003","authenticated-orcid":false,"given":"Sattam","family":"Alharbi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"}],"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":[[2025,12,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Blum, C., Roli, A., and Alba, E. (2005). An introduction to metaheuristic techniques. Parallel Metaheuristics, John Wiley & Sons.","DOI":"10.1002\/0471739383.ch1"},{"key":"ref_2","unstructured":"Epperson, J.F. (2013). An Introduction to Numerical Methods and Analysis, John Wiley & Sons."},{"key":"ref_3","first-page":"215","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":"Householder, A.S. (1970). The Numerical Treatment of a Single Nonlinear Equation, McGraw Hill Text."},{"key":"ref_5","unstructured":"Ostrowski, A. (1966). Solution of Equations and Systems of Equations, Academic Press."},{"key":"ref_6","unstructured":"Traub, J.F. 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