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In this study, we design a new efficient families of sixth-order iterative methods for solving scalar as well as system ofnonlinear equations. The main beauty of the proposed family is that we have to calculate only one inverse of the Jacobianmatrix in the case of nonlinear system which reduce the computational cost. The convergence properties are fully investigatedalong with two main theorems describing their order of convergence. In addition, we also presented a numerical work whichconfirm the order of convergence of the proposed family is well deduced for scalar as well as system of nonlinear equations.Further, we have also shown the the implementation of the proposed techniques on real world problems like, Van der Polequation, Hammerstein integral equation, etc.

Nonlinear equations and systems, iterative methods, Newton’s method, order of convergence