{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:54:58Z","timestamp":1740142498654,"version":"3.37.3"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T00:00:00Z","timestamp":1702339200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T00:00:00Z","timestamp":1702339200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Graduate Student Innovation Foundation Project of Bohai University"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61976027"],"award-info":[{"award-number":["61976027"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of Liaoning Province","award":["2022- MS-371","2023-MS-296"],"award-info":[{"award-number":["2022- MS-371","2023-MS-296"]}]},{"name":"Educational Commission Foundation of Liaoning Province of China","award":["LJKMZ20221492","LJKMZ20221498"],"award-info":[{"award-number":["LJKMZ20221492","LJKMZ20221498"]}]},{"name":"Key Project of Bohai University","award":["0522xn078"],"award-info":[{"award-number":["0522xn078"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2024,2]]},"DOI":"10.1007\/s40314-023-02517-1","type":"journal-article","created":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T13:03:43Z","timestamp":1702386223000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ball convergence analysis of Jarratt-type sixth-order method and its applications in solving some chemical problems"],"prefix":"10.1007","volume":"43","author":[{"given":"Wenshuo","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8524-6488","authenticated-orcid":false,"given":"Xiaofeng","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,12,12]]},"reference":[{"issue":"4","key":"2517_CR1","doi-asserted-by":"publisher","first-page":"841","DOI":"10.1007\/s10910-020-01113-6","volume":"58","author":"AS Alshomrani","year":"2020","unstructured":"Alshomrani AS, Behl R, Maroju P (2020) Local convergence of parameter based method with six and eighth order of convergence. J Math Chem 58(4):841\u2013853","journal-title":"J Math Chem"},{"issue":"12","key":"2517_CR2","doi-asserted-by":"publisher","first-page":"2894","DOI":"10.1002\/nme.6964","volume":"123","author":"I Angelo","year":"2022","unstructured":"Angelo I, Giulia S, Tommaso T (2022) An adaptive projection-based model reduction method for nonlinear mechanics with internal variables: application to thermo-hydro-mechanical systems. Int J Numer Mech Eng 123(12):2894\u20132918","journal-title":"Int J Numer Mech Eng"},{"issue":"7","key":"2517_CR3","doi-asserted-by":"publisher","first-page":"1958","DOI":"10.1007\/s10910-017-0823-z","volume":"56","author":"IK Argyros","year":"2018","unstructured":"Argyros IK, Gim\u00e9nez E, Magre\u00f1\u00e1n AA, Sarr\u00eda I, Sicilia JA (2018) Improved semilocal convergence analysis in Banach space with applications to chemistry. J Math Chem 56(7):1958\u20131975","journal-title":"J Math Chem"},{"issue":"2","key":"2517_CR4","doi-asserted-by":"publisher","first-page":"1913","DOI":"10.1007\/s40314-017-0429-x","volume":"37","author":"S Bhalla","year":"2018","unstructured":"Bhalla S, Kumar S, Argyros IK, Behl R, Motsa SS (2018) Higher-order modification of Steffensen\u2019s method for solving system of nonlinear equations. Comput Appl Math 37(2):1913\u20131940","journal-title":"Comput Appl Math"},{"issue":"3","key":"2517_CR5","doi-asserted-by":"publisher","first-page":"452","DOI":"10.3390\/math8030452","volume":"8","author":"G Candelario","year":"2020","unstructured":"Candelario G, Cordero A, Torregrosa JR (2020) Multipoint fractional iterative methods with $$(2\\alpha +1)$$th-order of convergence for solving nonlinear problems. Mathematics 8(3):452\u2013452","journal-title":"Mathematics"},{"issue":"12","key":"2517_CR6","doi-asserted-by":"publisher","first-page":"1221","DOI":"10.3390\/math7121221","volume":"7","author":"RR Capdevila","year":"2019","unstructured":"Capdevila RR, Cordero A, Torregrosa JR (2019) A new three-step class of iterative methods for solving nonlinear systems. Mathematics 7(12):1221\u20131221","journal-title":"Mathematics"},{"key":"2517_CR7","volume-title":"Numerical methods for chemical engineers with MATLAB applications","author":"A Constantinides","year":"1999","unstructured":"Constantinides A, Mostoufi N (1999) Numerical methods for chemical engineers with MATLAB applications. Prentice Hall, New York"},{"issue":"4","key":"2517_CR8","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1007\/s10910-020-01108-3","volume":"58","author":"A Cordero","year":"2020","unstructured":"Cordero A, Ramos H, Torregrosa JR (2020) Some variants of Halley\u2019s method with memory and their applications for solving several chemical problems. J Math Chem 58(4):751\u2013774","journal-title":"J Math Chem"},{"key":"2517_CR9","doi-asserted-by":"crossref","unstructured":"Elsisy MA, EISayed MA, (2019) Fuzzy rough bi-level multi-objective nonlinear programming problems. Alexandria Eng J 58(4):1471\u20131482","DOI":"10.1016\/j.aej.2019.12.002"},{"issue":"2","key":"2517_CR10","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1002\/cnm.1407","volume":"27","author":"GR Jolds","year":"2011","unstructured":"Jolds GR, Wittek A, Miller K (2011) An adaptive dynamic relaxation method for solving nonlinear finite element problems. Application to brain shift estimation. Int J Numer Methods Biomed Eng 27(2):173\u2013185","journal-title":"Int J Numer Methods Biomed Eng"},{"issue":"2","key":"2517_CR11","first-page":"880","volume":"184","author":"J Kou","year":"2006","unstructured":"Kou J, Li Y, Wang X (2006) Fourth-order iterative methods free from second derivative. Appl Math Comput 184(2):880\u2013885","journal-title":"Appl Math Comput"},{"issue":"15","key":"2517_CR12","doi-asserted-by":"publisher","first-page":"3154","DOI":"10.1080\/00207721.2022.2074568","volume":"53","author":"B Li","year":"2022","unstructured":"Li B, Yang X, Zhou R, Wen G (2022) Reinforcement learning-based optimised control for a class of second-order nonlinear dynamic systems. Int J Syst Sci 53(15):3154\u20133164","journal-title":"Int J Syst Sci"},{"issue":"3","key":"2517_CR13","first-page":"1021","volume":"51","author":"H Liao","year":"2023","unstructured":"Liao H (2023) A nonlinear optimization bifurcation tracking method for periodic solution of nonlinear systems. Mech Based Des Struct 51(3):1021\u20131225","journal-title":"Mech Based Des Struct"},{"issue":"7","key":"2517_CR14","doi-asserted-by":"publisher","first-page":"2117","DOI":"10.1007\/s10910-018-0856-y","volume":"56","author":"AA Magre\u00f1\u00e1n","year":"2018","unstructured":"Magre\u00f1\u00e1n AA, Argyros IK, Rainer JJ, Sicilia JA (2018) Ball convergence of a sixth-order newton-like method based on means under weak conditions. J Math Chem 56(7):2117\u20132131","journal-title":"J Math Chem"},{"issue":"3","key":"2517_CR15","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1007\/s10910-019-01097-y","volume":"58","author":"P Maroju","year":"2020","unstructured":"Maroju P, Magre\u00f1\u00e1n AA, Sarr\u00eda I, Kumar A (2020) Local convergence of fourth and fifth order parametric family of iterative methods in Banach spaces. J Math Chem 58(3):686\u2013705","journal-title":"J Math Chem"},{"key":"2517_CR16","volume-title":"Multipoint methods for solving nonlinear equations","author":"MS Petkovi\u0107","year":"2013","unstructured":"Petkovi\u0107 MS, Neta B, Petkovi\u0107 LD, D\u017euni\u0107 J (2013) Multipoint methods for solving nonlinear equations. Elsevier, New York"},{"issue":"11","key":"2517_CR17","doi-asserted-by":"publisher","first-page":"2099","DOI":"10.1016\/0009-2509(72)87067-2","volume":"27","author":"M Shacham","year":"1972","unstructured":"Shacham M, Kehat E (1972) An iteration method with memory for the solution of a non-linear equation. Chem Eng Sci 27(11):2099\u20132101","journal-title":"Chem Eng Sci"},{"key":"2517_CR18","doi-asserted-by":"publisher","unstructured":"Wang X, Chen X (2023) Dynamical behavior analysis of an eighth-order Sharma\u2019s method. Int J Biomath. https:\/\/doi.org\/10.1142\/S1793524523500687","DOI":"10.1142\/S1793524523500687"},{"issue":"2","key":"2517_CR19","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/s11075-014-9951-8","volume":"70","author":"X Wang","year":"2015","unstructured":"Wang X, Zhang T (2015) Efficient n-point iterative methods with memory for solving nonlinear equations. Numer Algorithms 70(2):357\u2013375","journal-title":"Numer Algorithms"},{"issue":"3","key":"2517_CR20","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1080\/09720502.2015.1033846","volume":"21","author":"X Wang","year":"2018","unstructured":"Wang X, Zhang T (2018) Efficient fifth-order iterative method for solving nonlinear systems. J Interdiscip Math 21(3):563\u2013577","journal-title":"J Interdiscip Math"},{"issue":"9","key":"2517_CR21","doi-asserted-by":"publisher","first-page":"22371","DOI":"10.3934\/math.20231141","volume":"8","author":"X Wang","year":"2023","unstructured":"Wang X, Yang Y, Qin Y (2023) Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems. AIMS Math 8(9):22371\u201322384","journal-title":"AIMS Math"},{"issue":"14","key":"2517_CR22","doi-asserted-by":"publisher","first-page":"7869","DOI":"10.1002\/mma.5384","volume":"43","author":"F Zafar","year":"2020","unstructured":"Zafar F, Cordero A, Torregrosa JR (2020) A family of optimal fourth-order methods for multiple roots of nonlinear equations. Math Methods Appl Sci 43(14):7869\u20137884","journal-title":"Math Methods Appl Sci"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-023-02517-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-023-02517-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-023-02517-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,11]],"date-time":"2024-02-11T11:20:00Z","timestamp":1707650400000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-023-02517-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,12]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["2517"],"URL":"https:\/\/doi.org\/10.1007\/s40314-023-02517-1","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2023,12,12]]},"assertion":[{"value":"1 July 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 November 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 November 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 December 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no conflicts of interest to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval"}},{"value":"All authors have read and agreed to the published version of the manuscript.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"18"}}