A Fourth-order Newton-type method free from second derivative for solving non-linear equations

Abstract

In this paper, we present a class of third-order Newton-type methods for solving non-linear equations by considering linear combination of two well-known third-order methods. Based on this, we obtain a fourth-order convergent method. The proposed approach is free from second derivatives. In each step, it only requires two evaluations of the given function and one evaluation of its first derivative. Analysis of efficiency demonstrates that the algorithm is superior and performs well. © 2011 Springer-Verlag Berlin Heidelberg.