Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown Multiplicity
In this paper, we investigate the local convergence of Schröder’s method for finding zeros of analytic functions with unknown multiplicity. Thus, we obtain a convergence theorem that provides exact domains of initial points together with error estimates to ensure the <i>Q</i>-quadratic c...
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| author | Plamena I. Marcheva Stoil I. Ivanov |
| author_facet | Plamena I. Marcheva Stoil I. Ivanov |
| author_sort | Plamena I. Marcheva |
| collection | DOAJ |
| description | In this paper, we investigate the local convergence of Schröder’s method for finding zeros of analytic functions with unknown multiplicity. Thus, we obtain a convergence theorem that provides exact domains of initial points together with error estimates to ensure the <i>Q</i>-quadratic convergence of Schröder’s method right from the first step. A comparison with the famous Newton’s method, based on the convergence and dynamics when it is applied to some polynomial and non-polynomial equations, is also provided. |
| format | Article |
| id | doaj-art-dd5b107397dc429eb09560fcf71e7ef9 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-dd5b107397dc429eb09560fcf71e7ef92025-01-24T13:39:59ZengMDPI AGMathematics2227-73902025-01-0113227510.3390/math13020275Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown MultiplicityPlamena I. Marcheva0Stoil I. Ivanov1Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, BulgariaFaculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, BulgariaIn this paper, we investigate the local convergence of Schröder’s method for finding zeros of analytic functions with unknown multiplicity. Thus, we obtain a convergence theorem that provides exact domains of initial points together with error estimates to ensure the <i>Q</i>-quadratic convergence of Schröder’s method right from the first step. A comparison with the famous Newton’s method, based on the convergence and dynamics when it is applied to some polynomial and non-polynomial equations, is also provided.https://www.mdpi.com/2227-7390/13/2/275iteration methodsSchröder’s methodlocal convergenceanalytic functionsbasins of attractionmultiple zeros |
| spellingShingle | Plamena I. Marcheva Stoil I. Ivanov Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown Multiplicity Mathematics iteration methods Schröder’s method local convergence analytic functions basins of attraction multiple zeros |
| title | Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown Multiplicity |
| title_full | Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown Multiplicity |
| title_fullStr | Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown Multiplicity |
| title_full_unstemmed | Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown Multiplicity |
| title_short | Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown Multiplicity |
| title_sort | convergence and dynamics of schroder s method for zeros of analytic functions with unknown multiplicity |
| topic | iteration methods Schröder’s method local convergence analytic functions basins of attraction multiple zeros |
| url | https://www.mdpi.com/2227-7390/13/2/275 |
| work_keys_str_mv | AT plamenaimarcheva convergenceanddynamicsofschrodersmethodforzerosofanalyticfunctionswithunknownmultiplicity AT stoiliivanov convergenceanddynamicsofschrodersmethodforzerosofanalyticfunctionswithunknownmultiplicity |