A necessary condition forBSI-stability
Copyright policy )A necessary condition forBSI-stability
This paper deals with a new stability concept - BSI-stability (internal BS-stability) introduced by \textit{R. Frank}, \textit{J. Schneid} and \textit{C. W. Ueberhuber} [Stability properties of implicit Runge-Kutta methods, SIAM J. Numer. Anal. 22, 497-534 (1985)] for s-stage implicit Runge-Kutta methods. The first part contains the definition of BSI-stability and a sufficient condition for it, given by Frank, Schneid, and Ueberhuber (loc. cit.). A necessary condition for BSI-stability is presented and proved in the second part. Finally in the third part this result is used to show that implicit Runge-Kutta methods based on the Lobatto quadrature (the Lobatto IIIC-methods) with more than two stages are not BSI-stable.
- Leiden University Netherlands
- University of Geneva Switzerland
- Heidelberg University Germany
implicit Runge-Kutta methods, necessary condition, Lobatto quadrature, Nonlinear ordinary differential equations and systems, Stability and convergence of numerical methods for ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations, internal BS-stability, ddc: ddc:510
implicit Runge-Kutta methods, necessary condition, Lobatto quadrature, Nonlinear ordinary differential equations and systems, Stability and convergence of numerical methods for ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations, internal BS-stability, ddc: ddc:510
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