Two algorithms to construct a consistent first order theory of equilibrium figures of close binary systems

Classical methods are based on the evaluation of the self-gravitational, centrifugal and tidal potentials. The most common technique used by classical methods shows convergence problems. To solve this problem up to first order in amplitudes two algorithms has been developed, the first one based on the Laplace method to develop the inverse of the distance and the second one based on the asymptotic properties of the numerical quadrature formulas.