Modified Potra–Pták Multi-step Schemes with Accelerated Order of Convergence for Solving Systems of Nonlinear Equations
Department of Mathematics, D.A.V. University, Sarmastpur, 144012 Jalandhar, India
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 Valencia, Spain
Author to whom correspondence should be addressed.
Received: 29 November 2018 / Revised: 22 December 2018 / Accepted: 23 December 2018 / Published: 27 December 2018
PDF [979 KB, uploaded 12 March 2019]
In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order Potra–Pták method and last is weighted-Newton step. Furthermore, we generalize our work to derive a family of multi-step iterative methods with order of convergence
The sixth order method is the special case of this multi-step scheme for
The family gives a four-step ninth order method for
As much higher order methods are not used in practice, so we study sixth and ninth order methods in detail. Numerical examples are included to confirm theoretical results and to compare the methods with some existing ones. Different numerical tests, containing academical functions and systems resulting from the discretization of boundary problems, are introduced to show the efficiency and reliability of the proposed methods.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Printed Edition Available!
A printed edition of this Special Issue is available here
Share & Cite This Article
MDPI and ACS Style
Arora, H.; Torregrosa, J.R.; Cordero, A. Modified Potra–Pták Multi-step Schemes with Accelerated Order of Convergence for Solving Systems of Nonlinear Equations. Math. Comput. Appl. 2019, 24, 3.
Arora H, Torregrosa JR, Cordero A. Modified Potra–Pták Multi-step Schemes with Accelerated Order of Convergence for Solving Systems of Nonlinear Equations. Mathematical and Computational Applications. 2019; 24(1):3.
Arora, Himani; Torregrosa, Juan R.; Cordero, Alicia. 2019. "Modified Potra–Pták Multi-step Schemes with Accelerated Order of Convergence for Solving Systems of Nonlinear Equations." Math. Comput. Appl. 24, no. 1: 3.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
Multiple requests from the same IP address are counted as one view.