Computational Modeling of Dynamical Systems

TL;DR

This paper discusses methods for computationally modeling dynamical systems with multiple time scales, enabling efficient long-term simulations by resolving fast dynamics and automating the modeling process.

Contribution

It introduces an automated approach to model dynamical systems with multiple time scales, demonstrated through two example problems.

Findings

Efficient simulation of systems with fast and slow dynamics.

Automated modeling process for multi-scale dynamical systems.

Successful application to oscillating and lattice models.

Abstract

In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be very costly. By resolving the fast time scales in a short time simulation, a model for the effect of the small time scale variation on large time scales can be determined, making solution possible on a long time interval. This process of computational modeling can be completely automated. Two examples are presented, including a simple model problem oscillating at a time scale of 1e-9 computed over the time interval [0,100], and a lattice consisting of large and small point masses.