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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 3204652, 6 pages
Research Article

Multistep High-Order Methods for Nonlinear Equations Using Padé-Like Approximants

Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain

Correspondence should be addressed to Juan R. Torregrosa; se.vpu.tam@errotrj

Received 23 May 2017; Accepted 29 August 2017; Published 3 October 2017

Academic Editor: Chuanxi Qian

Copyright © 2017 Alicia Cordero et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present new high-order optimal iterative methods for solving a nonlinear equation, , by using Padé-like approximants. We compose optimal methods of order 4 with Newton’s step and substitute the derivative by using an appropriate rational approximant, getting optimal methods of order 8. In the same way, increasing the degree of the approximant, we obtain optimal methods of order 16. We also perform different numerical tests that confirm the theoretical results.