Periodic Solutions of van der Pol's Equations with Large Damping Coefficientlambda = 0 sim 10

Abstract

A method of computing a periodic solution of van der Pol's equation is devised reducing the problem to the solution of a certain equation by means of Newton's method. For computing the value of the derivative necessary to apply Newton's method, the properties of variation of the orbit in the phase plane are used and, for step-by-step numerical integration of differential equations, a somewhat new method based on Stirling's interpolation formula combined with an ordinary Adams' extrapolating integration formula is used. The periodic solutions are actually computed for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda = 0 \sim 10</tex> and the minute but important change of the amplitude described by van der Pol's equation is found.