The disturbing function and the dissipative terms in Eqs. The integrations of Eqs. In this way, we use a four-dimensional iterative method to numerically solve the system of equations. If all real parts of the eigenvalues are negative the point is stable, but if at least one eigenvalue has a positive real part, the point is unstable. It must be noted that in the first order method the dissipative terms and are dropped from the Eqs.
Continuous line stands for the first order method and circles stand for numerical integrations.
After that, we take an average for each variable considering only the variations of the elements for the part of the stable planetesimal's orbit. We see that these numeric points match only the stable branch of the solutions. For this case, the developed method does not give good results due to its limitation as a first order theory in the planet's mass whereas extended corotation is strongly dependent on the planet's mass. This limitation brings about the deviations found in Fig. 3 . As a last example for an exterior resonance we show in Fig.