NUMERICAL INVESTIGATION OF THE PANTOGRAPH EQUATION

This paper presents some numerical examples concerning the pantograph equation y'(t) = ay(t) + by(qt) for different values of the parameters a, b, q, satisfying the conditions \a\ + b < 0, 0 < 1 - q much less t han 1. ''Naive'' interpretation of these examples could lead to wrong conclusion on the asymptotic behaviour of the exact solutions. Using a perturbation method and a recent result of Kuruklis, we analyze a sim ple numerical discretization of the pantograph equation. The main resu lt of this paper is that in order to see the correct asymptotic behavi our of the exact solution our numerical calculation has to go far beyo nd a certain critical point t, which depends on the parameters a, b a nd is inversely proportional to 1 - q. (C) 1997 Elsevier Science B.V.