  In this paper, we develop a class of robust numerical methods for solving
dynamical systems with multiple time scales. We first represent the solution of
a multiscale dynamical system as a transformation of a slowly varying solution.
Then, under the scale separation assumption, we provide a systematic way to
construct the transformation map and derive the dynamic equation for the slowly
varying solution. We also provide the convergence analysis of the proposed
method. Finally, we present several numerical examples, including ODE system
with three and four separated time scales to demonstrate the accuracy and
efficiency of the proposed method. Numerical results verify that our method is
robust in solving ODE systems with multiple time scale, where the time step
does not depend on the multiscale parameters.
