Integrating Vectors and Multiple Scales for Singularly Perturbed Ordinary Differential Equations

摘要

In this paper it will be shown that the (recently developed) perturbation method based on integrating vectors and multiple scales can also be applied to initial value problems for systems of singularly perturbed ordinary differential equations. Asymptotic approximations of first integrals can be obtained that are valid for all times. It will turn out that no matching principles are needed to obtain these asymptotic results. Several elementary examples are treated to show how this perturbation method can be applied.