# Efficient Simulation of Singularly Perturbed Systems Using a Stabilized Multirate Explicit Scheme

arXiv: https://arxiv.org/abs/2504.06371 · HTML: https://mlsanity.com/paper/2504.06371/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2025.

## Built on by (most cited first, 1 of 1)

- [Disentangling Slow and Fast Temporal Dynamics in Degradation Inference with Hierarchical Differential Models](https://mlsanity.com/paper/2509.00639/) (2025)

## Abstract (arXiv)

Singularly perturbed systems (SPSs) are prevalent in engineering applications, where numerically solving their initial value problems (IVPs) is challenging due to stiffness arising from multiple time scales. Classical explicit methods require impractically small time steps for stability, while implicit methods developed for SPSs are computationally intensive and less efficient for strongly nonlinear systems. This paper introduces a Stabilized Multirate Explicit Scheme (SMES) that stabilizes classical explicit methods without the need for small time steps or implicit formulations. By employing a multirate approach with variable time steps, SMES allows the fast dynamics to rapidly converge to their equilibrium manifold while slow dynamics evolve with larger steps. Analysis shows that SMES achieves numerical stability with significantly reduced computational effort and controlled error. Its effectiveness is illustrated with a numerical example.