دورية أكاديمية
Parametric Family of Root-Finding Iterative Methods: Fractals of the Basins of Attraction
| العنوان: | Parametric Family of Root-Finding Iterative Methods: Fractals of the Basins of Attraction |
|---|---|
| المؤلفون: | Padilla, José J., Chicharro, Francisco I., Cordero Barbero, Alicia, Torregrosa Sánchez, Juan Ramón |
| المساهمون: | Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros de Telecomunicación - Escola Tècnica Superior d'Enginyers de Telecomunicació, AGENCIA ESTATAL DE INVESTIGACION, European Regional Development Fund |
| بيانات النشر: | MDPI AG |
| سنة النشر: | 2022 |
| المجموعة: | Universitat Politécnica de Valencia: RiuNet / Politechnical University of Valencia |
| مصطلحات موضوعية: | Nonlinear problems, Iterative methods, Weight functions, Complex dynamics, Basin of attraction, Fractal, MATEMATICA APLICADA |
| الوصف: | [EN] Research interest in iterative multipoint schemes to solve nonlinear problems has increased recently because of the drawbacks of point-to-point methods, which need high-order derivatives to increase the order of convergence. However, this order is not the only key element to classify the iterative schemes. We aim to design new multipoint fixed point classes without memory, that improve or bring together the existing ones in different areas such as computational efficiency, stability and also convergence order. In this manuscript, we present a family of parametric iterative methods, whose order of convergence is four, that has been designed by using composition and weight function techniques. A qualitative analysis is made, based on complex discrete dynamics, to select those elements of the class with best stability properties on low-degree polynomials. This stable behavior is directly related with the simplicity of the fractals defined by the basins of attraction. In the opposite, particular methods with unstable performance present high-complexity in the fractals of their basins. The stable members are demonstrated also be the best ones in terms of numerical performance of non-polynomial functions, with special emphasis on Colebrook-White equation, with wide applications in Engineering. ; This research was partially supported by Grant PGC2018-095896-B-C22 funded by MCIN/AEI/10.13039/5011000113033 by "ERDF A way of making Europe", European Union. ; Padilla, JJ.; Chicharro, FI.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2022). Parametric Family of Root-Finding Iterative Methods: Fractals of the Basins of Attraction. Fractal and Fractional. 6(10):1-15. https://doi.org/10.3390/fractalfract6100572Test ; 1 ; 15 ; 6 ; 10 |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| تدمد: | 2504-3110 |
| العلاقة: | Fractal and Fractional; info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095896-B-C22/ES/DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIAL/; https://doi.org/10.3390/fractalfract6100572Test; http://hdl.handle.net/10251/192216Test; urn:eissn:2504-3110 |
| DOI: | 10.3390/fractalfract6100572 |
| الإتاحة: | https://doi.org/10.3390/fractalfract6100572Test http://hdl.handle.net/10251/192216Test |
| حقوق: | http://creativecommons.org/licenses/by/4.0Test/ ; info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsbas.F68E026E |
| قاعدة البيانات: | BASE |
| تدمد: | 25043110 |
|---|---|
| DOI: | 10.3390/fractalfract6100572 |