Spatially Partitioned Embedded Runge--Kutta Methods

David I. Ketcheson, Colin B. MacDonald, Steven J. Ruuth

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in nonembedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to nonphysical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted nonoscillatory spatial discretizations. Numerical experiments are provided to support the theory.
Original languageEnglish (US)
Pages (from-to)2887-2910
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number5
DOIs
StatePublished - Oct 30 2013

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