On a Three-Step Method with the Order of Convergence 1 + \( \sqrt{2} \) for the Solution of Systems of Nonlinear Operator Equations

Abstract

We propose a three-step modification of a method with an order of convergence 1+ \( \sqrt{2} \) aimed at the solution of nonlinear operator equations. We prove that the method is convergent and estimate its error. We also perform the numerical investigation of this modification on test examples, compare the results with the base method, and make conclusions on the basis of these results. The results of verification of the method confirm the theoretical predictions.