Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability
In this paper, a simple family of one-point iterative schemes for approximating the solutions of nonlinear equations, by using the procedure of weight functions, is derived. The convergence analysis is presented, showing the sufficient conditions for the weight function. Many known schemes are membe...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-05-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/8/2/55 |
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| author | Francisco I. Chicharro Alicia Cordero Neus Garrido Juan R. Torregrosa |
| author_facet | Francisco I. Chicharro Alicia Cordero Neus Garrido Juan R. Torregrosa |
| author_sort | Francisco I. Chicharro |
| collection | DOAJ |
| description | In this paper, a simple family of one-point iterative schemes for approximating the solutions of nonlinear equations, by using the procedure of weight functions, is derived. The convergence analysis is presented, showing the sufficient conditions for the weight function. Many known schemes are members of this family for particular choices of the weight function. The dynamical behavior of one of these choices is presented, analyzing the stability of the fixed points and the critical points of the rational function obtained when the iterative expression is applied on low degree polynomials. Several numerical tests are given to compare different elements of the proposed family on non-polynomial problems. |
| first_indexed | 2024-12-13T01:54:32Z |
| format | Article |
| id | doaj.art-b5ac3b155f0b417dbf32a004d0cd1cf1 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-13T01:54:32Z |
| publishDate | 2019-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-b5ac3b155f0b417dbf32a004d0cd1cf12022-12-22T00:03:25ZengMDPI AGAxioms2075-16802019-05-01825510.3390/axioms8020055axioms8020055Generating Root-Finder Iterative Methods of Second Order: Convergence and StabilityFrancisco I. Chicharro0Alicia Cordero1Neus Garrido2Juan R. Torregrosa3Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Avenida de La Paz 137, 26006 Logroño, SpainMultidisciplinary Mathematics Institute, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, SpainMultidisciplinary Mathematics Institute, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, SpainMultidisciplinary Mathematics Institute, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, SpainIn this paper, a simple family of one-point iterative schemes for approximating the solutions of nonlinear equations, by using the procedure of weight functions, is derived. The convergence analysis is presented, showing the sufficient conditions for the weight function. Many known schemes are members of this family for particular choices of the weight function. The dynamical behavior of one of these choices is presented, analyzing the stability of the fixed points and the critical points of the rational function obtained when the iterative expression is applied on low degree polynomials. Several numerical tests are given to compare different elements of the proposed family on non-polynomial problems.https://www.mdpi.com/2075-1680/8/2/55nonlinear equationsiterative methodconvergencebasin of attractionstability |
| spellingShingle | Francisco I. Chicharro Alicia Cordero Neus Garrido Juan R. Torregrosa Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability Axioms nonlinear equations iterative method convergence basin of attraction stability |
| title | Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability |
| title_full | Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability |
| title_fullStr | Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability |
| title_full_unstemmed | Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability |
| title_short | Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability |
| title_sort | generating root finder iterative methods of second order convergence and stability |
| topic | nonlinear equations iterative method convergence basin of attraction stability |
| url | https://www.mdpi.com/2075-1680/8/2/55 |
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