2025/12/03 by Thi Tam Dang, Dang, Thi Tam, Trung Hau Hoang +1
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2512.03679
openalex publication_date 2025/12/03 · openalex created_date 2025/12/05 · openalex updated_date 2026/07/28
In this paper, we investigate the application of exponential integrators to advection-dominated problems. We focus on Krylov subspace and Leja interpolation methods to compute the action of exponential and related matrix functions. Complementing our earlier paper, arXiv:2410.12765 (to appear in Advances in Applied Mathematics and Mechanics, 2025) based on a performance model, we extend the numerical investigation to higher-order Krylov approximations and new numerical regime, and assess their CPU-time efficiency relative to explicit Runge--Kutta schemes. We show that, depending on the problem setting, exponential integrators can either outperform or match explicit Runge--Kutta schemes. We also observe that Leja-based methods outperform Krylov iterations for large time steps, whereas for small time steps, Krylov-based methods provide better results than Leja-based methods.