Numerical solution of nonlinear equations by an optimal eighth-order class of iterative methods

摘要

Solving nonlinear equations by using iterative methods is discussed in this paper. An optimally convergent class of efficient three-point three-step methods without memory is suggested. Analytical proof for the class of methods is given to show the eighth-order convergence and also reveal its consistency with the conjecture of Kung and Traub. The beauty in the proposed methods from the class can be seen because of the optimization in important effecting factors, i.e. optimality order, lesser number of functional evaluations; as well as in viewpoint of efficiency index. The accuracy of some iterative methods from the proposed derivative-involved scheme is illustrated by solving numerical test problems and comparing with the available methods in the literatures.