An analytic-numerical method for computation of the Liapunov and period constants derived from their algebraic structure.

We consider the problem of computing the Liapunov and the period constants for a smooth differential equation with a nondegenerate critical point. Fir st, we investigate the structure of both constants when they are regarded a s polynomials on the coefficients of the differential equation. Second, we take advantage of this structure to derive a method to obtain the explicit expression of the above-mentioned constants. Although this method is based on the use of the Runge-Kutta-Fehlberg methods of orders 7 and 8 and the us e of Richardson's extrapolation, it provides the real expression for these constants.