Iterative methods for simultaneous computing arbitrary number of multiple zeros of nonlinear equations

Abstract

In this work, we present two modifications of an earlier presented iterative method for solving nonlinear equations in the case of multiple zeros. The new methods are two-point, derivative free iterative methods for the simultaneous extraction of one or several of the multiple zeros. We prove that the presented methods have quadratic convergence locally. Some numerical results with various nonlinear equations are given.

Keywords:

• nonlinear equations
• root-finding methods
• simultaneous methods
• order of convergence

2010 AMS Subject Classifications:

• 65H04
• 65H05

Acknowledgements

I thank the anonymous reviewers for their helpful and valuable suggestions that led to the improvement of this article. This work is supported by Shumen University under Grant RD-05-270/15.03.2012.