On the construction of three step derivative free four-parametric methods with accelerated order of convergence

In this paper, a general procedure to develop some four-parametric with-memory methods to find simple roots of nonlinear equations is proposed. The new methods are improved extensions of with derivative with- out memory iterative methods. We used four self-accelerating parameters to boost up the convergence order and computational efficiency of the proposed methods without using any additional function evaluations. Numerical examples are presented to support the theoretical results of the methods. We further investigate the dynamics of the methods in the complex plane.