Modeling thermodynamic equilibrium of complex nonlinear chemical systems with the most used Newton-Raphson method can lead to nonconvergence. From the mathematical properties of the set of equations, a chemically permitted interval is defined. By, imposing this interval, the robustness of the Newton-Raphson method is increased at a low computing time cost. The new method, the positive continuous fraction, does not depend on the first derivative of the objective function to find the solution. A new algorithm is thus built by the association of this very robust method with the fast Newton-Raphson method and the definition of the chemically allowed interval. This combined algorithm is very impressive in terms of reliability robustness, and speed.