Highly efficient family of iterative methods for solving nonlinear models

In this study, we present a new highly efficient sixth-order family of iterative methods for solving nonlinear equations along with convergence properties. Further, we extend this family to the multidimensional case preserving the same order of convergence. In order to illustrate the applicability of our methods, we choose some real world problems namely, kinematic syntheses, boundary value, Bratu's 2D, Fisher's and Hammerstein integral problems in the case of nonlinear systems (see Farhane et al., 2017 [1]; Kaur and Arora, 2017 [2] for more applications). In addition, numerical comparisons are made to show the performance of our iterative techniques with the existing ones. Moreover, we find that our techniques perform better as compared to the existing ones of same order in terms of residual error and the errors between two consecutive iterations. Finally, the stability analysis of our methods also support this to great extent.