ON A REFORMULATION OF THE MULTIPLE SCALES
PERTURBATION METHOD FOR DIFFERENCE
EQUATIONS
Wim van Horssen
In the classical multiple scales perturbation method for ordinary difference equations as developed in 1977 by Hoppensteadt and Miranker, difference equations are replaced at a certain moment in the perturbation procedure by ordinary differential equations.Taking into account the possibly different behavior of the solutions of a difference equation and of the solutions of a nearby differential equation, one can not always be sure that the constructed approximations by the Hoppensteadt-Miranker method indeed reflect the behavior of the exact solutions of the difference equations.For that reason an improved version of the multiple scales perturbation method for difference equations will be presented and formulated in this paper completely in terms of difference equations.