{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T19:49:56Z","timestamp":1760730596919,"version":"3.37.3"},"reference-count":35,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100006280","name":"Ministerio de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["MTM2011-28636-C02-02"],"award-info":[{"award-number":["MTM2011-28636-C02-02"]}],"id":[{"id":"10.13039\/501100006280","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>The dynamical behavior of different Steffensen-type methods is analyzed. We check the chaotic behaviors alongside the convergence radii (understood as the wideness of the basin of attraction) needed by Steffensen-type methods, that is, derivative-free iteration functions, to converge to a root and compare the results using different numerical tests. We will conclude that the convergence radii (and the stability) of Steffensen-type methods are improved by increasing the convergence order. The computer programming package M<jats:sc>ATHEMATICA<\/jats:sc>provides a powerful but easy environment for all aspects of numerics. This paper puts on show one of the application of this computer algebra system in finding fixed points of iteration functions.<\/jats:p>","DOI":"10.1155\/2014\/539707","type":"journal-article","created":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T17:02:56Z","timestamp":1394643776000},"page":"1-17","source":"Crossref","is-referenced-by-count":21,"title":["Basins of Attraction for Various Steffensen-Type Methods"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7462-9173","authenticated-orcid":true,"given":"Alicia","family":"Cordero","sequence":"first","affiliation":[{"name":"Instituto de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6905-8951","authenticated-orcid":true,"given":"Fazlollah","family":"Soleymani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan R.","family":"Torregrosa","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5829-8634","authenticated-orcid":true,"given":"Stanford","family":"Shateyi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","first-page":"64","volume":"16","year":"1933","journal-title":"Skandinavisk Aktuarietidskrift"},{"issue":"1","key":"2","first-page":"27","volume":"72","year":"2011","journal-title":"International Journal of Pure and Applied Mathematics"},{"issue":"2","key":"3","doi-asserted-by":"crossref","first-page":"255","DOI":"10.18514\/MMN.2011.303","volume":"12","year":"2011","journal-title":"Miskolc Mathematical Notes"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.04.058"},{"first-page":"xviii+310","year":"1964","series-title":"Prentice-Hall Series in Automatic Computation","key":"5"},{"year":"1964","key":"6"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2012.04.017"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2013.02.035"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2013.05.002"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2013.11.017"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s00010-004-2733-y"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2012.12.075"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2013.03.012"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.12.013"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2013.02.042"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/301718"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2009.06.041"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01401018"},{"issue":"7","key":"19","first-page":"1701","volume":"1","year":"2006","journal-title":"Scholarpedia"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1984-15240-6"},{"year":"1992","key":"21"},{"year":"2009","key":"22","first-page":"xxiv+467"},{"year":"2010","key":"23"},{"year":"2004","key":"25","first-page":"xii+332"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1007\/BF03025310"},{"key":"28","first-page":"45","volume":"6","year":"2011","journal-title":"General Mathematics Notes"},{"issue":"1","key":"29","first-page":"247","volume":"13","year":"2012","journal-title":"Fixed Point Theory"},{"key":"30","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1145\/321850.321860","volume":"21","year":"1974","journal-title":"Journal of the Association for Computing Machinery"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.2307\/1971408"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1985-15391-1"},{"key":"33","first-page":"3","volume":"10","year":"2004","journal-title":"Scientia. 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