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Zero-finder methods derived using Runge–Kutta techniques

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
217
Issue
12
Identifiers
DOI: 10.1016/j.amc.2010.11.059
Keywords
  • Nonlinear Equations
  • Iterative Methods
  • Order Of Convergence
  • Efficiency
Disciplines
  • Mathematics

Abstract

Abstract In this paper some families of zero-finding iterative methods for nonlinear equations are presented. The key idea to derive them is to solve an initial value problem applying Runge–Kutta techniques. More explicitly, these methods are used to solve the problem that consists in a differential equation in what appears the inverse function of the one which zero will be computed and the condition given by the value attained by it at the initial approximation. Carrying out this procedure several families of different orders of local convergence are obtained. Furthermore, the efficiency of these families are computed and two new families using like-Newton’s methods that improve the most efficient one are also given.

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