Stability Analysis of Simple Root Seeker for Nonlinear Equation
In this paper, the stability of a class of Liu–Wang’s optimal eighth-order single-parameter iterative methods for solving simple roots of nonlinear equations was studied by applying them to arbitrary quadratic polynomials. Under the Riemann sphere and scaling theorem, the complex dynamic behavior of...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/2/215 |
| _version_ | 1827758595223060480 |
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| author | Xiaofeng Wang Wenshuo Li |
| author_facet | Xiaofeng Wang Wenshuo Li |
| author_sort | Xiaofeng Wang |
| collection | DOAJ |
| description | In this paper, the stability of a class of Liu–Wang’s optimal eighth-order single-parameter iterative methods for solving simple roots of nonlinear equations was studied by applying them to arbitrary quadratic polynomials. Under the Riemann sphere and scaling theorem, the complex dynamic behavior of the iterative method was analyzed by fractals. We discuss the stability of all fixed points and the parameter spaces starting from the critical points with the Mathematica software. The dynamical planes of the elements with good and bad dynamical behavior are given, and the optimal parameter element with stable behavior was obtained. Finally, a numerical experiment and practical application were carried out to prove the conclusion. |
| first_indexed | 2024-03-11T09:09:39Z |
| format | Article |
| id | doaj.art-1673eea469c4436589f41fd8cb3627a4 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T09:09:39Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-1673eea469c4436589f41fd8cb3627a42023-11-16T19:06:54ZengMDPI AGAxioms2075-16802023-02-0112221510.3390/axioms12020215Stability Analysis of Simple Root Seeker for Nonlinear EquationXiaofeng Wang0Wenshuo Li1School of Mathematical Sciences, Bohai University, Jinzhou 121013, ChinaSchool of Mathematical Sciences, Bohai University, Jinzhou 121013, ChinaIn this paper, the stability of a class of Liu–Wang’s optimal eighth-order single-parameter iterative methods for solving simple roots of nonlinear equations was studied by applying them to arbitrary quadratic polynomials. Under the Riemann sphere and scaling theorem, the complex dynamic behavior of the iterative method was analyzed by fractals. We discuss the stability of all fixed points and the parameter spaces starting from the critical points with the Mathematica software. The dynamical planes of the elements with good and bad dynamical behavior are given, and the optimal parameter element with stable behavior was obtained. Finally, a numerical experiment and practical application were carried out to prove the conclusion.https://www.mdpi.com/2075-1680/12/2/215nonlinear problemsiterative methodscomplex dynamics behaviorstabilitydynamical plane |
| spellingShingle | Xiaofeng Wang Wenshuo Li Stability Analysis of Simple Root Seeker for Nonlinear Equation Axioms nonlinear problems iterative methods complex dynamics behavior stability dynamical plane |
| title | Stability Analysis of Simple Root Seeker for Nonlinear Equation |
| title_full | Stability Analysis of Simple Root Seeker for Nonlinear Equation |
| title_fullStr | Stability Analysis of Simple Root Seeker for Nonlinear Equation |
| title_full_unstemmed | Stability Analysis of Simple Root Seeker for Nonlinear Equation |
| title_short | Stability Analysis of Simple Root Seeker for Nonlinear Equation |
| title_sort | stability analysis of simple root seeker for nonlinear equation |
| topic | nonlinear problems iterative methods complex dynamics behavior stability dynamical plane |
| url | https://www.mdpi.com/2075-1680/12/2/215 |
| work_keys_str_mv | AT xiaofengwang stabilityanalysisofsimplerootseekerfornonlinearequation AT wenshuoli stabilityanalysisofsimplerootseekerfornonlinearequation |