KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Numerical Mathematics Group
Preprint Posting Date2020-01-14
Online Publication Date2020-07-09
Print Publication Date2020-07
Embargo End Date2021-07-09
Permanent link to this recordhttp://hdl.handle.net/10754/661682
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AbstractThe recently-introduced relaxation approach for Runge–Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior of implicit and explicit relaxation Runge–Kutta methods in this context. We find that, in addition to their useful conservation property, the relaxation methods yield other improvements. Experiments show that their solutions bear stronger qualitative similarity to the true solution and that the error grows more slowly in time. We also prove that these methods are superconvergent for a certain class of Hamiltonian systems.
CitationRanocha, H., & Ketcheson, D. I. (2020). Relaxation Runge–Kutta Methods for Hamiltonian Problems. Journal of Scientific Computing, 84(1). doi:10.1007/s10915-020-01277-y
SponsorsResearch reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). The authours would like to thank Ernst Hairer for a discussion of symplecticity and the preservation of phase space volume.
PublisherSpringer Science and Business Media LLC
JournalJournal of Scientific Computing