{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:03:56Z","timestamp":1760231036899,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T00:00:00Z","timestamp":1661126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union","award":["PGC2018-095896-B-C22"],"award-info":[{"award-number":["PGC2018-095896-B-C22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We present a new Jarratt-type family of optimal fourth- and sixth-order iterative methods for solving nonlinear equations, along with their convergence properties. The schemes are extended to nonlinear systems of equations with equal convergence order. The stability properties of the vectorial schemes are analyzed, showing their symmetric wide sets of converging initial guesses. To illustrate the applicability of our methods for the multidimensional case, we choose some real world problems such as kinematic syntheses, boundary value problems, Fisher\u2019s and Hammerstein\u2019s integrals, etc. Numerical comparisons are given to show the performance of our schemes, compared with the existing efficient methods.<\/jats:p>","DOI":"10.3390\/sym14081742","type":"journal-article","created":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T05:18:17Z","timestamp":1661145497000},"page":"1742","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["New Iterative Schemes to Solve Nonlinear Systems with Symmetric Basins of Attraction"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7462-9173","authenticated-orcid":false,"given":"Alicia","family":"Cordero","sequence":"first","affiliation":[{"name":"Multidisciplinary Mathematics Institute, Universitat Polit\u00e8cnica de Valen\u00e8ncia, Camino de Vera s\/n, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Smmayya","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan"}],"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":"Multidisciplinary Mathematics Institute, Universitat Polit\u00e8cnica de Valen\u00e8ncia, Camino de Vera s\/n, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0552-2783","authenticated-orcid":false,"given":"Fiza","family":"Zafar","sequence":"additional","affiliation":[{"name":"Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,22]]},"reference":[{"key":"ref_1","unstructured":"Ostrowski, A.M. 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