EIGHTH ORDER STEFFENSEN TYPE NUMERICAL METHOD FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS

Abstract

In this project, we discussed a derivative free three-step family of eighth-order Steffensen type numerical methods for solving systems of nonlinear equations. The local convergence order of the family is determined using first-order divided difference operator for functions of several variables, and thereafter, direct computation by Taylor series expansion which helps to develop the scheme based on with higher computational efficiency index requires less computational time in computing. Computational efficiency is discussed and a comparison between the efficiencies of the proposed technique with the existing ones is made. We have illustrated numerically that the proposed method converges with eighth-order accuracy coinciding with the theoretical analysis. Moreover, the efficiency of the method is illustrated by solving different test problems. According to our experiments, the proposed eighth-order method provides more accurate solutions than the existing fourth-order, sixth order and seventh order Steffensen type method. We can find that the proposed method gets better approximate solution. It is shown that the new family is especially efficient in solving large systems.