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Local Convergence Balls for Nonlinear Problems with Multiplicity and Their Extension to Eighth-Order Convergence
- Source :
- Mathematical Problems in Engineering, Vol 2019 (2019), RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia, Universidad de Alicante (UA)
- Publication Year :
- 2019
- Publisher :
- Hindawi Limited, 2019.
-
Abstract
- [EN] The main contribution of this study is to present a new optimal eighth-order scheme for locating zeros with multiplicity m > 1. An extensive convergence analysis is presented with the main theorem in order to demonstrate the optimal eighth-order convergence of the proposed scheme. Moreover, a local convergence study for the optimal fourth-order method defined by the first two steps of the new method is presented, allowing us to obtain the radius of the local convergence ball. Finally, numerical tests on some real-life problems, such as a Van der Waals equation of state, a conversion Chemical engineering problem and two standard academic test problems are presented, which confirm the theoretical results established in this paper and the efficiency of this proposed iterative method. We observed from the numerical experiments that our proposed iterative methods have good values for convergence radii. Further, they have not only faster convergence towards the desired zero of the involved function but they also have both smaller residual error and a smaller difference between two consecutive iterations than current existing techniques.<br />This research was partially supported by Ministerio de Economia y Competitividad under grant MTM2014-52016-C2-2-P and by the project of Generalitat Valenciana Prometeo/2016/089.
- Subjects :
- Van der Waals equation
Non linear equations
Article Subject
Iterative method
General Mathematics
Efficiency index
010103 numerical & computational mathematics
Residual
Computer Science::Digital Libraries
01 natural sciences
symbols.namesake
Applied mathematics
0101 mathematics
Multiple roots
Mathematics
Optimal iterative method
lcsh:Mathematics
General Engineering
Multiplicity (mathematics)
Radius
lcsh:QA1-939
Local convergence
010101 applied mathematics
Nonlinear system
lcsh:TA1-2040
Computer Science::Mathematical Software
Ball (bearing)
symbols
MATEMATICA APLICADA
lcsh:Engineering (General). Civil engineering (General)
Subjects
Details
- Language :
- English
- ISSN :
- 15635147
- Volume :
- 2019
- Database :
- OpenAIRE
- Journal :
- Mathematical Problems in Engineering
- Accession number :
- edsair.doi.dedup.....d1ecb89bc0262ebac8f57c4dd974306b