On stability and conservation properties of (S)epirk integrators in the context of discretized pdes

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

Abstract

Exponential integrators are becoming increasingly popular for stiff problems of high dimension due to their attractive property of solving the linear part of the system exactly and hence being A-stable. In practice, however, exponential integrators are implemented using approximation techniques to matrix-vector products involving functions of the matrix exponential (the so-called ϕ-functions) to make them efficient and competitive to other state-of-the-art schemes. We will examine linear stability and provide a Courant–Friedrichs–Lewy (CFL) condition of special classes of exponential integrator schemes called EPIRK and sEPIRK and demonstrate their dependence on the parameters of the embedded approximation technique. Furthermore, a conservation property of the EPIRK schemes is proven.

Details

Authors
Organisations
External organisations
  • University of Kassel
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematical Analysis

Keywords

  • A-stability, CFL condition, Conservation, Exponential integrators
Original languageEnglish
Title of host publicationTheory, Numerics and Applications of Hyperbolic Problems II
PublisherSpringer New York LLC
Pages617-629
Number of pages13
Volume237
ISBN (Print)9783319915470
Publication statusPublished - 2018 Jan 1
Publication categoryResearch
Peer-reviewedYes
Event16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 - Aachen, Germany
Duration: 2016 Aug 12016 Aug 5

Conference

Conference16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016
CountryGermany
CityAachen
Period2016/08/012016/08/05