General efficient class of Steffensen type methods with memory for solving systems of nonlinear equations

Abstract

There are a very small number of high quality derivative free methods with memory for solving a system of nonlinear equations numerically. Motivated and inspired by the fact, we propose a more efficient general class of Steffensen type multipoint methods with memory. This proposed class requires one divided difference and inverse of only one matrix per full iteration. We also demonstrate their applicability and illustrate that these methods produce approximations of greater accuracy and remarkably reduce the computational time for solving systems of nonlinear equations numerically. For quantitative comparison, we have also computed total number of convergent points and convergent percentage along with basins of attractions on a number of test problems to recommend the best quality algorithm.