A modification of Chebyshev-Halley method free from second derivatives for nonlinear equations

Document Type: Research articles


Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran


‎In this paper‎, ‎we present a new modification of Chebyshev-Halley‎
‎method‎, ‎free from second derivatives‎, ‎to solve nonlinear equations‎.
‎The convergence analysis shows that our modification is third-order‎
‎convergent‎. ‎Every iteration of this method requires one function and‎
‎two first derivative evaluations‎. ‎So‎, ‎its efficiency index is‎
‎$3^{1/3}=1.442$ that is better than that of Newton method‎. ‎Several‎
‎numerical examples are given to illustrate the performance of the‎
‎presented method‎.