Accelerated methods of order for systems of nonlinear equations

We present a new iterative method of order of convergence 5, for solving nonlinear systems, by composing the Midpoint method with Newton’s method and using an approximation for the Jacobian matrix in order to reduce the required number of functional evaluations per iteration. In addition, we compare the efficiency index of these methods with that of Newton’s method and present several numerical tests, which confirm the theoretical results and allow us to compare these variants with Newton’s method.