On the periodic solution of the van der Pol equation for small values of the damping parameter

✍ Scribed by Buonomo, A.

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 146 KB
• Volume: 26
• Category: Article
• ISSN: 0098-9886
• DOI: 10.1002/(sici)1097-007x(199801/02)26:1<39::aid-cta6>3.0.co;2-x

✦ Synopsis

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 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 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 (2•70 of *0.