Abstract:

In this paper, we present a new family of optimal eighthorder iterative methods for solving nonlinear equations by using weight function approach. Per iteration the new methods need to compute three functional evaluations and one evaluation of firstorder derivative, which implies that the efficiency index of the new method is 1.682. Numerical results shown that, comparing with the other iterative methods, our iterative methods have higher convergence order and calculation precision.

Key words:  nonlinear equations, optimal order, eighthorder convergence, iterative method, rootfinding