A new two-step biparametric family of sixth-order iterative methods free from second derivatives for solving nonlinear algebraic equations

摘要

In this paper, a new two-step biparametric family of sixth-order iterative methods free from second derivatives are proposed in this paper to find a simple root of a nonlinear algebraic equation. Their efficiency indices are all found to be 61/4. Convergence analysis together with numerical experiments confirms sixth-order convergence and asymptotic error constants.