Computational Modeling of Dynamical Systems
For researchers simulating stiff dynamical systems, this offers an automated method to handle multiple time scales, though it is an incremental extension of existing multi-scale modeling techniques.
The paper presents an automated computational modeling approach for dynamical systems with multiple time scales, enabling efficient long-time simulation by resolving fast scales in short simulations. It demonstrates the method on a problem oscillating at 1e-9 over [0,100] and a lattice with varying masses.
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.