On Convergence of a Novel Jacobian-Free Parametric Iterative Vectorial Schemes

In this work, we have proposed a Jacobian free iterative vectorial multiparametric family for solving systems of nonlinear equations. The scheme is obtained by replacing the Jacobian matrix by divided difference operator in a family of third and fourth order iterative methods which maintains the convergence order. This way we avoid the expensive inversion of the inverse of the Jacobian which may not even exist. Moreover, the efficiency index of the method is studied in detail. The comparisons of the numerical experiments of the proposed family and other competitive methods corroborate the utility of presented method over the existing ones.