DESIGN AND ANALYSIS OF AN EFFICIENT MULTI STEP ITERATIVE SCHEME FOR SYSTEMS OF NONLINEAR EQUATIONS.

In this paper, an efficient sixth order multi step method is proposed in Banach spaces and its local convergence is studied in order to approximate a locally unique solution of a nonlinear or a system of nonlinear equations. Based on Lipschitz's continuity condition, new convergence analysis provides radius of convergence, bounds on error and estimates on the uniqueness of solution under assumptions on the first derivative only. Hence, the method can be applied to a wider class of functions that expands its applicability. Numerical examples are presented to illustrate the theoretical results. In the end, the basins of attraction are given to show the convergence behavior in complex plane. [ABSTRACT FROM AUTHOR]