TY - JOUR
T1 - Strong Stability Preserving Runge–Kutta and Linear Multistep Methods
AU - Izzo, Giuseppe
AU - Jackiewicz, Zdzislaw
N1 - Funding Information:
The work of the first author (GI) was supported by INdAM Research group GNCS.
Publisher Copyright:
© 2022, The Author(s).
PY - 2022/12
Y1 - 2022/12
N2 - This paper reviews strong stability preserving discrete variable methods for differential systems. The strong stability preserving Runge–Kutta methods have been usually investigated in the literature on the subject, using the so-called Shu–Osher representation of these methods, as a convex combination of first-order steps by forward Euler method. In this paper, we revisit the analysis of strong stability preserving Runge–Kutta methods by reformulating these methods as a subclass of general linear methods for ordinary differential equations, and then using a characterization of monotone general linear methods, which was derived by Spijker in his seminal paper (SIAM J Numer Anal 45:1226–1245, 2007). Using this new approach, explicit and implicit strong stability preserving Runge–Kutta methods up to the order four are derived. These methods are equivalent to explicit and implicit RK methods obtained using Shu–Osher or generalized Shu–Osher representation. We also investigate strong stability preserving linear multistep methods using again monotonicity theory of Spijker.
AB - This paper reviews strong stability preserving discrete variable methods for differential systems. The strong stability preserving Runge–Kutta methods have been usually investigated in the literature on the subject, using the so-called Shu–Osher representation of these methods, as a convex combination of first-order steps by forward Euler method. In this paper, we revisit the analysis of strong stability preserving Runge–Kutta methods by reformulating these methods as a subclass of general linear methods for ordinary differential equations, and then using a characterization of monotone general linear methods, which was derived by Spijker in his seminal paper (SIAM J Numer Anal 45:1226–1245, 2007). Using this new approach, explicit and implicit strong stability preserving Runge–Kutta methods up to the order four are derived. These methods are equivalent to explicit and implicit RK methods obtained using Shu–Osher or generalized Shu–Osher representation. We also investigate strong stability preserving linear multistep methods using again monotonicity theory of Spijker.
KW - General linear methods
KW - Linear multistep methods
KW - Monotonicity
KW - Runge–Kutta methods
KW - SSP coefficient
KW - Shu–Osher representation
KW - Strong stability preserving
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U2 - 10.1007/s41980-022-00731-x
DO - 10.1007/s41980-022-00731-x
M3 - Article
AN - SCOPUS:85143431027
SN - 1018-6301
VL - 48
SP - 4029
EP - 4062
JO - Bulletin of the Iranian Mathematical Society
JF - Bulletin of the Iranian Mathematical Society
IS - 6
ER -