2025/04/08 by Yibo Shi, Shi, Yibo, Cristian R. Rojas +1 · 1 citation
Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #FOS: Electrical engineering #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2504.06371
openalex publication_date 2025/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.