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Properties of Runge...
Properties of Runge-Kutta-Summation-By-Parts methods
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- Linders, Viktor (författare)
- Linköpings universitet,Lund University,Lunds universitet,Numerisk analys,Forskargrupper vid Lunds universitet,Numerical Analysis,Lund University Research Groups,Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa, Israel,Beräkningsmatematik,Tekniska fakulteten
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- Nordström, Jan, 1953- (författare)
- Linköpings universitet,Linköping University,Department of Mathematics and Applied Mathematics, University of Johannesburg, South Africa,Beräkningsmatematik,Tekniska fakulteten
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- Frankel, Steven H. (författare)
- Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa, Israel
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(creator_code:org_t)
- Elsevier BV, 2020
- 2020
- Engelska.
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 419
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Abstract
Ämnesord
Stäng
- We review and extend the list of stability and convergence properties satisfied by Runge-Kutta (RK) methods that are associated with Summation-By-Parts (SBP) operators, herein called RK-SBP methods. The analysis covers classical, generalized as well as upwind SBP operators. Previous work on the topic has relied predominantly on energy estimates. In contrast, we derive all results using a purely algebraic approach that rests on the well-established theory of RK methods. The purpose of this paper is to provide a bottom-up overview of stability and convergence results for linear and non-linear problems that relate to general RK-SBP methods. To this end, we focus on the RK viewpoint, since this perspective so far is largely unexplored. This approach allows us to derive all results as simple consequences of the properties of SBP methods combined with well-known results from RK theory. In this way, new proofs of known results such as A-, L- and B-stability are given. Additionally, we establish previously unreported results such as strong S-stability, dissipative stability and stiff accuracy of certain RK-SBP methods. Further, it is shown that a subset of methods are B-convergent for strictly contractive non-linear problems and convergent for non-linear problems that are both contractive and dissipative.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- B-convergence
- Dissipative stability
- Runge-Kutta methods
- S-stability
- SBP in time
- Stiff accuracy
- SBP in time
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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