New Iterative Schemes to Solve Nonlinear Systems with Symmetric Basins of Attraction

We present a new Jarratt-type family of optimal fourth- and sixth-order iterative methods for solving nonlinear equations, along with their convergence properties. The schemes are extended to systems equations equal order. stability properties the vectorial analyzed, showing symmetric wide sets converging initial guesses. To illustrate applicability our multidimensional case, we choose some real world problems such as kinematic syntheses, boundary value problems, Fisher’s Hammerstein’s integrals, etc. Numerical comparisons given show performance schemes, compared existing efficient methods.