Title: A three-step iterative method for non-linear systems with sixth order of convergence

Authors: Fazlollah Soleymani

Addresses: Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract: A new method for finding the numerical solution of non-linear systems of equations is suggested and analysed. The proposed scheme includes three steps and 2n + 2n² function evaluations in solving an n × n non-linear system. The analysis of convergence releases the sixth order of convergence, while the whole scheme is free from second order Frechet derivative. In order to show the efficiency of the new method, some numerical experiments will be employed. The results are in harmony with the theoretical aspects.

Keywords: nonlinear systems; three-step method; matrix; Frechet derivative; COC; computational order of convergence; sixth order of convergence; iterative methods.

DOI: 10.1504/IJCSM.2013.058057

International Journal of Computing Science and Mathematics, 2013 Vol.4 No.4, pp.363 - 373

Received: 10 Nov 2012
Accepted: 04 May 2013

Published online: 01 Dec 2013 *

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