{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T10:09:57Z","timestamp":1778926197053,"version":"3.51.4"},"reference-count":25,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,16]],"date-time":"2021-05-16T00:00:00Z","timestamp":1621123200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PGC2018-095896-B-C22 (MCIU\/AEI\/FEDER, UE)"],"award-info":[{"award-number":["PGC2018-095896-B-C22 (MCIU\/AEI\/FEDER, UE)"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A general optimal iterative method, for approximating the solution of nonlinear equations, of (n+1) steps with 2n+1 order of convergence is presented. Cases n=0 and n=1 correspond to Newton\u2019s and Ostrowski\u2019s schemes, respectively. The basins of attraction of the proposed schemes on different test functions are analyzed and compared with the corresponding to other known methods. The dynamical planes showing the different symmetries of the basins of attraction of new and known methods are presented. The performance of different methods on some test functions is shown.<\/jats:p>","DOI":"10.3390\/sym13050884","type":"journal-article","created":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T02:31:34Z","timestamp":1621218694000},"page":"884","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A General Optimal Iterative Scheme with Arbitrary Order of Convergence"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7462-9173","authenticated-orcid":false,"given":"Alicia","family":"Cordero","sequence":"first","affiliation":[{"name":"Multidisciplinary Institute of Mathematics, Universitat Polit\u00e8nica de Val\u00e8ncia, 46022 Val\u00e8ncia, 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":"Multidisciplinary Institute of Mathematics, Universitat Polit\u00e8nica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7319-9992","authenticated-orcid":false,"given":"Paula","family":"Triguero-Navarro","sequence":"additional","affiliation":[{"name":"Multidisciplinary Institute of Mathematics, Universitat Polit\u00e8nica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Amat, S., and Busquier, S. 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