Finding Approximate Roots of Nonlinear Equations by Using New Sixth-Order Convergence

Abstract

In this study, we introduced new iterative techniques, for the purpose solving nonlinear equations. The new approaches are based on the auxiliary equation and Newton's method, respectively. Our method's a convergence analysis is explained. The novel approach is found to have convergence order of six. Numerical experiments show that the new method work better than well-known iterative methods and is similar to them.