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

الملخص

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. 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.