Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions

Abstract

In the present paper, we consider a construction proposed in Xiao and Yin (2016) to improve the order of convergence of the method from p to p + 2m under weaker assumptions. Using the idea of restricted convergence domains we extend the applicability of the method considered by Xiao and Yin (2016). Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.

Keywords

• newton’s method
• radius of convergence
• local convergence