New families of nonlinear third-order solvers for finding multiple roots

Authors:
Changbum Chun;Hwa ju Bae;Beny Neta
Affiliations:
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea;Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea;Naval Postgraduate School, Department of Applied Mathematics, Monterey, CA 93943, United States
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In this paper, we present two new families of iterative methods for multiple roots of nonlinear equations. One of the families require one-function and two-derivative evaluation per step, and the other family requires two-function and one-derivative evaluation. It is shown that both are third-order convergent for multiple roots. Numerical examples suggest that each family member can be competitive to other third-order methods and Newton's method for multiple roots. In fact the second family is even better than the first.