Seventh and Twelfth-Order Iterative Methods for Roots of Nonlinear Equations

This study presents two iterative methods, based on Newton’s method, to attain the numerical solutions of nonlinear equations. We prove that our methods have seven and twelve orders of convergence. The analytical investigation has been established to show that our schemes have higher efficiency indexes than some recent methods. Numerical examples are executed to investigate the performance of the proposed schemes. Moreover, the theoretical order of convergence is verified on the numerical examples