Stability analysis of Jacobian-free iterative methods for solving nonlinear systems by using families of mth power divided differences

The dynamical properties of a family of forward, central divided differences and Richardson extrapolation technique are studied. Applying these tools, an iterative method for solving nonlinear systems can be transformed in a Jacobian-free scheme. We analyze the dynamical behavior of new schemes obtained in this way on low degree polynomial systems. Several chemical problems are solved by using these new techniques, confirming the theoretical results. In one of these problems (Chandrasekhar H-equation), a degenerated case with singular Jacobian is analyzed, obtaining good results.