On the construction of numerical iterative schemes of any order of convergence for solving nonlinear systems of equations

Abstract

This paper presents a methodology for constructing iterative schemes of any order of convergence for solving nonlinear systems of equations. It also provides formulas for the order of convergence of any iterative schemes constructed using the method proposed in this paper. A test case is conducted numerically for the second and third order of convergence using a computer algebra system called Maxima. The code used is listed at the end of the test case.