Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes

Willem Hundsdorfer, Anna Mozartova, Valeriu Savcenco

Research output: Chapter in Book/Report/Conference proceedingChapter

8 Scopus citations


Multirate schemes for conservation laws or convection-dominated problems seem to come in two flavors: schemes that are locally inconsistent, and schemes that lack mass-conservation. In this paper these two defects are discussed for one-dimensional conservation laws. Particular attention will be given to monotonicity properties of the multirate schemes, such as maximum principles and the total variation diminishing (TVD) property. The study of these properties will be done within the framework of partitioned Runge-Kutta methods. It will also be seen that the incompatibility of consistency and mass-conservation holds for ‘genuine’ multirate schemes, but not for general partitioned methods.
Original languageEnglish (US)
Title of host publicationRecent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws
PublisherSpringer Nature
Number of pages19
ISBN (Print)9783642332203
StatePublished - 2013
Externally publishedYes


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