Newton-like methods for solving nonlinear equations

A continuous method was developed for solving nonlinear equations with large-scale stability using the homotopy method. Newton-like iterative methods and Steffensen-Newton-like iterative methods were developed by discretization of the method. The large-scale convergence for Newton-like iterative methods has quadratic convergence. The convergence factors for weak convergence for Newton-like iterative methods and Steffensen-Newton-like iterative methods were found using Taylors series expansions. Newton-like iterative methods remove the strict condition f' (x) ≠ 0 imposed on f(x) and have parameters to adjust the convergence rate. The Steffensen-Newton-like iterative methods do not use derivatives, so they have advantages over Newton's method and the Newton-down hill method.