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

作者：Chun Changbum; Bae Hwa ju; Neta Beny^*

来源：Computers & Mathematics with Applications, 2009, 57(9): 1574-1582.

DOI：10.1016/j.camwa.2008.10.070

• Newton's method
• Multiple roots
• Iterative methods
• Nonlinear equations
• Order of convergence
• Root-finding

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. Published by Elsevier Ltd

• 出版日期2009-5