Construction and Dynamics of Efficient High-Order Methods for Nonlinear Systems

Abstract

In this paper, we derive new multi-parametric families of iterative methods whose orders range from six to eight, for solving nonlinear systems. Based on a generating function method known in the literature, we construct these families in the most general way possible in order to include some well-known methods as special cases. Several applied problems are solved to check the performance of our methods and other existing ones and to verify the theoretical results. It is found that our methods are competitive in performance compared to the other methods. Moreover, the basin of attraction method is introduced for nonlinear systems to confirm our findings and to choose the best performers.