Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Preprint Posting Date2019-09-29
Online Publication Date2020-11-24
Print Publication Date2020-01
Permanent link to this recordhttp://hdl.handle.net/10754/659989
MetadataShow full item record
AbstractMany 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.
CitationRanocha, 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:10.1137/19m1290346
SponsorsResearch 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.