Variants of Newton’s Method using fifth-order quadrature formulas

Some variants of Newton’s method are developed in this work in order to solve nonlinear equations depending on one or several variables, based in rules of quadrature of fifth order. We prove the third or fifth order of convergence of these methods for dimension one, and the second or third order in several variables, depending on the behaviour of the second derivative. Moreover, different numeric tests confirm or improve theoretic results and allow us to compare these variants with Newton’s classical method.