TY - JOUR
T1 - Strong stability preserving implicit–explicit transformed general linear methods
AU - Izzo, Giuseppe
AU - Jackiewicz, Zdzislaw
N1 - Funding Information:
The work of this author was partially supported by GNCS-INdAM, Italy.
Publisher Copyright:
© 2019 International Association for Mathematics and Computers in Simulation (IMACS)
PY - 2020/10
Y1 - 2020/10
N2 - We consider the class of implicit–explicit (IMEX) general linear methods (GLMs) to construct methods where the explicit part has strong stability preserving (SSP) property, while the implicit part of the method has inherent Runge–Kutta stability (IRKS) property, and it is A-, or L-stable. We will also investigate the absolute stability of these methods when the implicit and explicit parts interact with each other. In particular, we will monitor the size of the region of absolute stability of the IMEX scheme, assuming that the implicit part of the method is A(α)-stable for α∈[0,π∕2]. Finally we furnish examples of SSP IMEX GLMs up to the order p=4 and stage order q=p with optimal SSP coefficients.
AB - We consider the class of implicit–explicit (IMEX) general linear methods (GLMs) to construct methods where the explicit part has strong stability preserving (SSP) property, while the implicit part of the method has inherent Runge–Kutta stability (IRKS) property, and it is A-, or L-stable. We will also investigate the absolute stability of these methods when the implicit and explicit parts interact with each other. In particular, we will monitor the size of the region of absolute stability of the IMEX scheme, assuming that the implicit part of the method is A(α)-stable for α∈[0,π∕2]. Finally we furnish examples of SSP IMEX GLMs up to the order p=4 and stage order q=p with optimal SSP coefficients.
KW - Construction of highly stable methods
KW - General linear methods
KW - IMEX methods
KW - Inherent Runge–Kutta stability
KW - SSP property
KW - Stability analysis
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U2 - 10.1016/j.matcom.2019.11.008
DO - 10.1016/j.matcom.2019.11.008
M3 - Article
AN - SCOPUS:85076217432
SN - 0378-4754
VL - 176
SP - 206
EP - 225
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -