Performance Evaluation of Stabilized Corrections for Mixed Precision Runge--Kutta Methods

[2607.10967] Performance Evaluation of Stabilized Corrections for Mixed Precision Runge--Kutta Methods Skip to main content Search Submit Donate Log in Mathematics > Numerical Analysis arXiv:2607.10967 (math) [Submitted on 13 Jul 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Performance Evaluation of Stabilized Corrections for Mixed Precision Runge--Kutta Methods Authors: César Herrera , John Driscoll , Sigal Gottlieb , Zachary J. Grant , Tej Sai Kakumanu , Andrew Christlieb View PDF Abstract: Mixed precision Runge--Kutta methods reduce the cost of the expensive implicit solves in diagonally implicit Runge--Kutta (DIRK) schemes by evaluating them in low precision, while retaining the accuracy of the scheme for larger time steps. The accuracy lost to the low-precision perturbation can be recovered through inexpensive explicit corrections; however, these corrections have an adverse impact on stability. Recently proposed stabilized corrections remedy this by applying a stabilization matrix to the correction step, but their runtime cost has not previously been quantified. In this work, we present a numerical study of the runtime performance of these stabilized corrections. Using spectral semi-discretizations of two nonlinear partial differential equations, the inviscid Burgers' equation and the porous medium equation, we compare uncorrected mixed precision DIRK methods against explicitly corrected and stabilized variants across half, single, double, and quadruple precision pairings, for SDIRK methods of orders two through four. We report convergence, runtime, and speedups, and show that the stabilized corrections improve the accuracy of the mixed precision schemes while preserving substantial runtime savings. All experiments were performed on an Intel Xeon Platinum 8480+ CPU with Julia version 1.11.4. Subjects: Numerical Analysis (math.NA) Cite as: arXiv:2607.10967 [math.NA] (or arXiv:2607.10967v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2607.10967 Focus to learn more arXiv-issued DOI via DataCite Submission history From: César Herrera [ view email ] [v1] Mon, 13 Jul 2026 00:25:42 UTC (1,578 KB) [v2] Tue, 25 Aug 2026 08:33:41 UTC (1,578 KB) Full-text links: Access Paper: View PDF TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2026-07 Change to browse by: cs cs.NA math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

Related documents

• Performance Evaluation of Stabilized Corrections for Mixed Precision Runge--Kutta Methods#670683
• Exploring Exponential Runge-Kutta Methods: A Survey#163161
• On the reliability and stability of direct explicit Runge-Kutta integrators#680576
• 0701 Accuracy Improvement of a Time Integration Scheme for Vortex Method#69687
• Convergence of a Ramshaw-Mesina Iteration#799815