New uni-parametric family of multipoint methods with memory for systems of nonlinear equations

Abstract

Based on McDougall and Wotherspoon method (Appl Math Lett 29:20–25, 2014) for solving a scalar nonlinear equation, we present a new uni-parametric family of multipoint methods with memory for solving systems of nonlinear equations numerically. The proposed family requires only one Jacobian inversion per iterate and is obtained by using the weight function approach. It is proved that the proposed methods are more efficient than the existing methods, particularly when the size of the nonlinear system is large and high accuracy is required.