{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/energy-stability-of-explicit-runge-kutta","title":"Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems","arxiv_id":"1909.13215","date":"2019-09-29","proceeding":null,"authors":["Hendrik Ranocha","David I. Ketcheson"],"abstract":"Many important initial value problems have the property that energy is non-increasing in time. Energy stable methods, also referred to as strongly stable methods, guarantee the same property discretely. We investigate requirements for conditional energy stability of explicit Runge-Kutta methods for nonlinear or non-autonomous problems. We provide both necessary and sufficient conditions for energy stability over these classes of problems. Examples of conditionally energy stable schemes are constructed and an example is given in which unconditional energy stability is obtained with an explicit scheme.","url_abs":"http://arxiv.org/abs/1909.13215v2","url_pdf":"http://arxiv.org/pdf/1909.13215v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"energy-stability-of-explicit-runge-kutta","repo_url":"https://github.com/ranocha/EnergyStabilityExplicitRungeKuttaNonlinearNonautonomous","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}