Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems
Type
ArticleAuthors
Ranocha, Hendrik
Ketcheson, David I.

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
Date
2020-11-24Preprint Posting Date
2019-09-29Online Publication Date
2020-11-24Print Publication Date
2020-01Submitted Date
2019-09-30Permanent link to this record
http://hdl.handle.net/10754/659989
Metadata
Show full item recordAbstract
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.Citation
Ranocha, H., & Ketcheson, D. I. (2020). Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems. SIAM Journal on Numerical Analysis, 58(6), 3382–3405. doi:10.1137/19m1290346Sponsors
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.arXiv
1909.13215Additional Links
https://epubs.siam.org/doi/10.1137/19M1290346ae974a485f413a2113503eed53cd6c53
10.1137/19m1290346