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Local Convergence Balls for Nonlinear Problems with Multiplicity and Their Extension to Eighth-Order Convergence
Joint Authors
Alshomrani, Ali Saleh
Cevallos, Fabricio
Behl, Ramandeep
Martínez, Eulalia
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-01-02
Country of Publication
Egypt
No. of Pages
17
Main Subjects
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 not only have faster convergence towards the desired zero of the involved function but also have both smaller residual error and a smaller difference between two consecutive iterations than current existing techniques.
American Psychological Association (APA)
Behl, Ramandeep& Martínez, Eulalia& Cevallos, Fabricio& Alshomrani, Ali Saleh. 2019. Local Convergence Balls for Nonlinear Problems with Multiplicity and Their Extension to Eighth-Order Convergence. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-17.
https://search.emarefa.net/detail/BIM-1194337
Modern Language Association (MLA)
Behl, Ramandeep…[et al.]. Local Convergence Balls for Nonlinear Problems with Multiplicity and Their Extension to Eighth-Order Convergence. Mathematical Problems in Engineering No. 2019 (2019), pp.1-17.
https://search.emarefa.net/detail/BIM-1194337
American Medical Association (AMA)
Behl, Ramandeep& Martínez, Eulalia& Cevallos, Fabricio& Alshomrani, Ali Saleh. Local Convergence Balls for Nonlinear Problems with Multiplicity and Their Extension to Eighth-Order Convergence. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-17.
https://search.emarefa.net/detail/BIM-1194337
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1194337