Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence
Journal of Numerical Analysis and Approximation Theory, 2021 We present a local convergence analysis Potra-Ptak-type method with optimal fourth order of convergence in order to approximate a solution of a nonlinear equation. In earlier studies such as [1], [5]-[28] hypotheses up to the fourth derivative are used.
Ioannis K. Argyros, Santhosh George
doaj +11 more sources
Numerical‐Computational Model for Nonlinear Analysis of Frames with Semirigid Connection
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 A numerical‐computational model for static analysis of plane frames with semirigid connections and geometric nonlinear behavior is presented. The set of nonlinear equations governing the structural system is solved by the Potra–Pták method in an incremental procedure, with order of cubic convergence, combined with the linear arc‐length path‐following ...
Luiz Antonio Farani de Souza +3 more
wiley +1 more source
Optimal High‐Order Methods for Solving Nonlinear Equations
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 A class of optimal iterative methods for solving nonlinear equations is extended up to sixteenth‐order of convergence. We design them by using the weight function technique, with functions of three variables. Some numerical tests are made in order to confirm the theoretical results and to compare the new methods with other known ones.
S. Artidiello +4 more
wiley +1 more source
Third‐Order Newton‐Type Methods Combined with Vector Extrapolation for Solving Nonlinear Systems
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 We present a third‐order method for solving the systems of nonlinear equations. This method is a Newton‐type scheme with the vector extrapolation. We establish the local and semilocal convergence of this method. Numerical results show that the composite method is more robust and efficient than a number of Newton‐type methods with the other vector ...
Wen Zhou, Jisheng Kou, Vinay Kanwar
wiley +1 more source
Potra‐Pták Iterative Method with Memory
International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014 The problem is to extend the method proposed by Soleymani et al. (2012) to a method with memory. Following this aim, a free parameter is calculated using Newton’s interpolatory polynomial of the third degree. So the R‐order of convergence is increased from 4 to 6 without any new function evaluations.
Taher Lotfi +4 more
wiley +1 more source
On Some Efficient Techniques for Solving Systems of Nonlinear Equations
Advances in Numerical Analysis, Volume 2013, Issue 1, 2013., 2013 We present iterative methods of convergence order three, five, and six for solving systems of nonlinear equations. Third‐order method is composed of two steps, namely, Newton iteration as the first step and weighted‐Newton iteration as the second step.
Janak Raj Sharma +2 more
wiley +1 more source
Iterative Fixed‐Point Methods for Solving Nonlinear Problems: Dynamics and Applications
, 2014 Abstract and Applied Analysis, Volume 2014, Issue 1, 2014.
Juan R. Torregrosa +3 more
wiley +1 more source
Extended convergence analysis of the Newton–Potra method under weak conditions
Applicationes Mathematicae, 2021Ioannis K Argyros +2 more
exaly
An optimized derivative-free form of the Potra–Pták method
Mathematical and Computer Modelling, 2012Fazlollah Soleymani +2 more
exaly
High-resolution structure of a new crystal form of BamA POTRA4–5 fromEscherichia coli
Acta Crystallographica Section F: Structural Biology Communications, 2011Heng Zhang, Zengqiang Gao, Lan-Fen Li
exaly