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

A class of robust numerical methods for solving dynamical systems with multiple time scales