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Journal of Applied Mathematics
Volume 2014, Article ID 737305, 7 pages
http://dx.doi.org/10.1155/2014/737305
Research Article

A New Biparametric Family of Two-Point Optimal Fourth-Order Multiple-Root Finders

Department of Applied Mathematics, Dankook University, Cheonan 330-714, Republic of Korea

Received 21 February 2014; Revised 17 June 2014; Accepted 20 June 2014; Published 14 September 2014

Academic Editor: Juan R. Torregrosa

Copyright © 2014 Young Ik Kim and Young Hee Geum. 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.

Abstract

We construct a biparametric family of fourth-order iterative methods to compute multiple roots of nonlinear equations. This method is verified to be optimally convergent. Various nonlinear equations confirm our proposed method with order of convergence of four and show that the computed asymptotic error constant agrees with the theoretical one.