Abstract: A new fourth and third order one-point iterative methods for finding zeros of nonlinear equations are presented. In terms of computational cost, the new iterative method requires four evaluations of functions per iteration. It is shown and proved that the new one-point methods have a convergence of order four and three. We examine the effectiveness of the new methods by approximating the multiple roots of nonlinear equations. Numerical comparisons are made to show the performance of the new one-point iterative methods and thus verifies the theoretical results.
Keywords: Newton-type methods; One-point; Multiple roots; Nonlinear equations; Root-finding; Order of convergence.