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

Authors:
Fazlollah Soleymani
Affiliations:
Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Venue:
International Journal of Computing Science and Mathematics
Year:
2013

Citing 3
Cited 0

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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.