ASYMPTOTIC REPRESENTATION OF THE CYCLE OF VAN DER POL'S EQUATION FOR SMALL DAMPING COEFFICIENTS,

The limit cycle of Van der Pols equation is expanded as a power series of the damping coefficient epsilon, the coefficients being finite trigonometric sums with the time as argument. Because the development was implemented in a fully automatic way on a computer, it has been pushed to a high power of epsilon. Hence, for epsilon as large as 0.75, the estimates given by the series for the amplitude and the period agree to 15 decimal places with their correct values computed on integrating by recurrent power series Van der Pols equation and its associated variational equation. When epsilon reaches 1.75, the agreement is still within 0.001. Author