On the Hybridization of the Double Step Length Method for Solving System of Nonlinear Equations

Abstract

A hybrid derivative-free double step length technique is proposed in this work in order to enhance the numerical results and convergence properties of the double direction and step length scheme. This is accomplished by combining a Picard-Mann hybrid iterative method proposed by Khan [Fix Point Theory and Applications, pp. 1-10, vol.69 (2013)] with the double step length approach. A derivative line search is employed in order to compute the two step lengths. Furthermore, a suitable acceleration parameter is developed to approximate the Jacobian matrix. Under some mild conditions, the proposed method is shown to converge globally. The numerical experiment presented in this paper illustrates the efficiency of the proposed method over some existing methods.