The Dynamics of a Continuous Newton-like Method

Manoj K. Singh and Ioannis K. Argyros ()
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Manoj K. Singh: College of Technology, Sardar Vallabhbhai Patel University of Agriculture and Technology, Meerut 250110, India
Ioannis K. Argyros: Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

Mathematics, 2022, vol. 10, issue 19, 1-14

Abstract: The objective of the current work is to invent and introduce the continuous version of Newton’s method. This scheme is used to establish some interesting properties with examples. We have plotted the fractal pattern graphs for a Newton-like method and a Damped Newton-like method in the discrete case and hence we have introduced a new concept of streamline for the continuous version of the Newton-like method. The graph and streamlines of these patterns are in agreement with numerical results and describe the convergence and stability of the proposed method to different roots when the Newton method fails.

Keywords: continuation Newton-like method; iteration function; order of convergence; basin of attraction; fractal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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