Authors:Mouhamad Al-Sayed, Samuel Bernard (MUSICS, ICJ), Arsène Marzorati (DRACULA, BEAGLE, MMCS, MUSICS, ICJ, BIOTIC), Jonathan Rouzaud-Cornabas (BIOTIC, CITI, INSA Lyon)
Abstract:Mixed-precision methods combine low and high precision arithmetics to exploit low precision computational speed and high precision accuracy. Large ODE systems that contain many heterogeneous interactions lead to a high computational cost that could be tackled with mixed-precision solvers. We tested mixedprecision versions of the Bogacki-Shampine 3(2) Runge-Kutta pair over three benchmark systems: coupled linear oscillators, the Kuramoto model and a circadian clock model. Our study is performed in a way that can be adapted to any finite-precision format, software architecture and numerical scheme. We found that mixed-precision solvers can preserve most of the high-precision solver accuracy under a wide range of solver tolerances. Moreover, mixed-precision solver accuracy improves with system size, reaching levels equivalent to high-precision solvers in small system size. We also observed that mixed-precision arithmetic does not impact the number of evaluation in a way that balances the benefit of fast operations in low precision. Taken together, these results show that mixed-precision methods can offer significant computational speed-up at little or no loss of accuracy in large coupled ODE systems.
| Comments: | Preprint of an article submitted to SIAM Journal on Scientific Computing (under revision) |
| Subjects: | Numerical Analysis (math.NA) |
| Cite as: | arXiv:2605.23727 [math.NA] |
| (or arXiv:2605.23727v1 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.23727 arXiv-issued DOI via DataCite (pending registration) |
From: Arsene Marzorati [view email] [via CCSD proxy]
[v1]
Fri, 22 May 2026 15:06:42 UTC (918 KB)
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