Local convergence of parameter based method with six and eighth order of convergence

This paper dealt with the local convergence study of the parameter based sixth and eighth order iterative method. This analysis discuss under assumption that the first order Fréchet derivative satisfied the Lipschitz continuity condition. In this way, we also proposed the theoretical radius of convergence of these methods. Finally, some numerical examples demonstrate that our results apply to compute the radius of convergence ball of iterative method to solve nonlinear equations. We compare the results with the method in Kumar et al. (J Comput Appl Math 330:676–694, 2018) and observe that by our approach we get much larger balls as existing ones.