Premium
On the periodic solution of the van der Pol equation for small values of the damping parameter
Author(s) -
Buonomo A.
Publication year - 1998
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/(sici)1097-007x(199801/02)26:1<39::aid-cta6>3.0.co;2-x
Subject(s) - van der pol oscillator , mathematics , power series , radius of convergence , mathematical analysis , series (stratigraphy) , padé approximant , decimal , convergence (economics) , physics , quantum mechanics , paleontology , arithmetic , nonlinear system , economics , biology , economic growth
We give a purely analytical perturbation method of solution of the van der Pol equation, whereby the periodic solution can be actually developed in the form of a power series in the damping parameter ε up to any desired order and thus analysed in detail. The coefficients of the series solution, which are given in explicit form by recurrent analytical formulae, are calculated up to the order ε 500 to accurately determine the radius of convergence of the series solution, for which the value of 1·89 (correct to two decimal places) was found. We have then investigated the well‐known Shohat expansion in order to elucidate an unsolved question concerning its validity, which we show to be restricted to the narrower interval ε<2·70 of ε⩾0. © 1998 John Wiley & Sons, Ltd.