Oscillatory Systems with Three Separated Time Scales: Analysis and Computation

摘要

We study a few interesting issues that occur in multiscale modeling and computation for oscillatory dynamical systems that involve three or more separated scales. A new type of slow variables which do not formally have bounded derivatives emerge from averaging in the fastest time scale. We present a few systems which have such new slow variables and discuss their characterization. The examples motivate a numerical multiscale algorithm that uses nested tiers of integrators which numerically solve the oscillatory system on different time scales. The communication between the scales follows the framework of the Heterogeneous Multiscale Method. The method's accuracy and efficiency are evaluated and its applicability is demonstrated by examples.