Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems

Hendrik Ranocha, David I. Ketcheson

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Many important initial value problems have the property that energy is nonincreasing 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 nonautonomous 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.
Original languageEnglish (US)
Pages (from-to)3382-3405
Number of pages24
JournalSIAM Journal on Numerical Analysis
Issue number6
StatePublished - Nov 24 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-12-08
Acknowledgements: Research reported in this publication was supported by the King Abdullah University of Scienceand Technology (KAUST). The first author was partially supported by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) under Grant SO 363/14-1.


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