{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:07:49Z","timestamp":1760234869321,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T00:00:00Z","timestamp":1624838400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research (DSR) at King 107 Abdulaziz University, Jeddah, Saudi Arabia","award":["KEP-MSc-49-130-42"],"award-info":[{"award-number":["KEP-MSc-49-130-42"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Symmetries are important in studying the dynamics of physical systems which in turn are converted to solve equations. Jarratt\u2019s method and its variants have been used extensively for this purpose. That is why in the present study, a unified local convergence analysis is developed of higher order Jarratt-type schemes for equations given on Banach space. Such schemes have been studied on the multidimensional Euclidean space provided that high order derivatives (not appearing on the schemes) exist. In addition, no errors estimates or results on the uniqueness of the solution that can be computed are given. These problems restrict the applicability of the methods. We address all these problems by using the first order derivative (appearing only on the schemes). Hence, the region of applicability of existing schemes is enlarged. Our technique can be used on other methods due to its generality. Numerical experiments from chemistry and other disciplines of applied sciences complete this study.<\/jats:p>","DOI":"10.3390\/sym13071162","type":"journal-article","created":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T13:39:22Z","timestamp":1624887562000},"page":"1162","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Convergence of Higher Order Jarratt-Type Schemes for Nonlinear Equations from Applied Sciences"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1505-8945","authenticated-orcid":false,"given":"Ramandeep","family":"Behl","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ioannis K.","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fouad Othman","family":"Mallawi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christopher I.","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Oklahoma, Norman, OK 73071, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,28]]},"reference":[{"key":"ref_1","unstructured":"Traub, J.F. (1964). Iterative Methods for the Solution of Equations, American Mathematical Soc."},{"key":"ref_2","unstructured":"Ostrowski, A.M. (1960). Solutions of Equations and System of Equations, Academic Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1145\/321850.321860","article-title":"Optimal order of one-point and multi-point iteration","volume":"21","author":"Kung","year":"1974","journal-title":"J. ACM"},{"key":"ref_4","first-page":"119","article-title":"Some efficient fourth order multipoint methods for solving equations","volume":"9","author":"Jarratt","year":"1969","journal-title":"Nord. Tidskr. Inf. Behandl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1090\/S0025-5718-66-99924-8","article-title":"Some fourth order multipoint iterative methods for solving equations","volume":"20","author":"Jarratt","year":"1966","journal-title":"Math. Comp."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1137\/0710072","article-title":"A family of fourth order methods for nonlinear equations","volume":"10","author":"King","year":"1973","journal-title":"SIAM J. Numer. Anal."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/BF00373799","article-title":"A pseudo-spectral solution of 2-parameter Bratu\u2019s equation","volume":"6","author":"Kapania","year":"1990","journal-title":"Comput. Mech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s11075-016-0152-5","article-title":"Local convergence and the dynamics of a two-point four parameter Jarratt-like method under weak conditions","volume":"74","author":"Amat","year":"2017","journal-title":"Numer. Algorith."},{"key":"ref_9","unstructured":"Argyros, I.K. (2008). Convergence and Application of Newton-Type Iterations, Springer."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Argyros, I.K., and Hilout, S. (2013). Numerical Methods in Nonlinear Analysis, World Scientific Publ. Comp.","DOI":"10.1142\/8475"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s11075-009-9342-8","article-title":"On new iterative method for solving systems of nonlinear equations","volume":"54","author":"Awawdeh","year":"2010","journal-title":"Numer. Algor."},{"key":"ref_12","first-page":"147","article-title":"A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics","volume":"357","author":"Bahl","year":"2019","journal-title":"Appl. Math. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.advwatres.2017.09.027","article-title":"The 1D Richards\u2019 equation in two layered soils: A Filippov approach to treat discontinuities","volume":"115","author":"Berardi","year":"2018","journal-title":"Adv. Water Resour."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2255","DOI":"10.1137\/100786320","article-title":"A Nested Newton-Type Algorithm for Finite Volume Methods Solving Richards\u2019 Equation in Mixed Form","volume":"32","author":"Casulli","year":"2010","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1155\/2013\/780153","article-title":"Drawing dynamical and parameter planes of iterative families and methods","volume":"2013","author":"Chicharro","year":"2013","journal-title":"Sci. World J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1016\/j.aml.2013.03.012","article-title":"Chaos in King\u2019s iterative family","volume":"26","author":"Cordero","year":"2013","journal-title":"Appl. Math. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1461","DOI":"10.1007\/s10910-016-0724-6","article-title":"Multidimensional stability analysis of a family of biparametric iterative methods","volume":"55","author":"Cordero","year":"2017","journal-title":"J. Math. Chem."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6457532","DOI":"10.1155\/2017\/6457532","article-title":"Efficient high-order iterative methods for solving nonlinear systems and their application on heat conduction problems","volume":"2017","author":"Cordero","year":"2017","journal-title":"Complexity"},{"key":"ref_19","first-page":"26","article-title":"Stability analysis of a parametric family of iterative methods for solving nonlinear models","volume":"285","author":"Cordero","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"ref_20","first-page":"398","article-title":"Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension","volume":"244","author":"Cordero","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"ref_21","first-page":"686","article-title":"Variants of Newton\u2019s method using fifth-order quadrature formulas","volume":"190","author":"Cordero","year":"2007","journal-title":"Appl. Math. Comput."},{"key":"ref_22","first-page":"120","article-title":"A sixth-order family of three-point modified newton-like multiple-root finders and the dynamics behind their extraneous fixed points","volume":"283","author":"Geum","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2688","DOI":"10.1016\/j.cam.2009.11.017","article-title":"Dynamics of a new family of iterative processes for quadratic polynomials","volume":"233","author":"Romero","year":"2010","journal-title":"J. Comput. Appl. Math."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"822","DOI":"10.1080\/00207160.2012.663081","article-title":"Dynamics of a fifth-order iterative method","volume":"89","author":"Plaza","year":"2012","journal-title":"Int. J. Comput. Math."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1007\/s10596-020-09949-2","article-title":"Iterative schemes for surfactant transport in porous media","volume":"25","author":"Illiano","year":"2021","journal-title":"Comput. Geosci."},{"key":"ref_26","first-page":"29","article-title":"Different anomalies in a Jarratt family of iterative root-finding methods","volume":"233","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Petkovi\u0107, M.S., Neta, B., Petkovi\u0107, L.D., and Dz\u0306uni\u0107, J. (2013). Multipoint Methods for Solving Nonlinear Equations, Academic Press.","DOI":"10.1016\/B978-0-12-397013-8.00002-9"},{"key":"ref_28","first-page":"129","article-title":"An adaptive continuation process for solving systems of nonlinear equations","volume":"3","author":"Rheinboldt","year":"1978","journal-title":"Pol. Acad. Sci. Banach Ctr. Publ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s40324-016-0085-x","article-title":"Improved Newton-like methods for solving systems of nonlinear equations","volume":"74","author":"Sharma","year":"2017","journal-title":"SeMA J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1137\/0712034","article-title":"A method for the numerical determination of bifurcation states of nonlinear systems of equations","volume":"12","author":"Simpson","year":"1975","journal-title":"SIAM J. Numer. Anal."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2465","DOI":"10.1016\/j.nonrwa.2009.08.003","article-title":"On locating all roots of systems of nonlinear equations inside bounded domain using global optimization methods","volume":"11","author":"Tsoulos","year":"2010","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0893-9659(00)00100-2","article-title":"A variant of Newton\u2019s method with accelerated third order convergence","volume":"13","author":"Weerakoon","year":"2000","journal-title":"Appl. Math. Lett."},{"key":"ref_33","first-page":"125849","article-title":"Higher order Jarratt-like iterations for solving system of nonlinear equations","volume":"395","author":"Zhanlav","year":"2021","journal-title":"Appl. Math. Comput."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/7\/1162\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:25:53Z","timestamp":1760163953000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/7\/1162"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,28]]},"references-count":33,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["sym13071162"],"URL":"https:\/\/doi.org\/10.3390\/sym13071162","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,6,28]]}}}