Accession Number : AD0649562

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

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s) : Deprit,Andre ; Rom,A. R. M.

Report Date : FEB 1967

Pagination or Media Count : 26

Abstract : The limit cycle of Van der Pol's 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 Pol's equation and its associated variational equation. When epsilon reaches 1.75, the agreement is still within 0.001. (Author)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, *POWER SERIES), ASYMPTOTIC SERIES, NUMERICAL ANALYSIS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE