TY - JOUR
T1 - A new class of strong stability preserving general linear methods
AU - Braś, Michał
AU - Izzo, Giuseppe
AU - Jackiewicz, Zdzisław
N1 - Funding Information:
The work of the first author (M. Bra?) was partially supported by the Faculty of Applied Mathematics AGH UST, Poland statutory tasks within subsidy of Ministry of Science and Higher Education.
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/11
Y1 - 2021/11
N2 - We systematically investigate strong stability preserving general linear methods of order p, stage order q=p or q=p−1, with r=p+1 external approximations, and s=p−1 internal approximations, for numerical solution of differential systems. Examples of methods of order p and stage order q=p or q=p−1, with large strong stability preserving coefficients and large regions of absolute stability, are provided for p=2, p=3, and p=4. The results of numerical experiments confirm that the methods constructed in this paper achieve the expected order of accuracy, do not produce spurious oscillations, and they are suitable to preserve the monotonicity of the numerical solution, when applied to discretization of hyperbolic conservation laws with discontinuous initial conditions.
AB - We systematically investigate strong stability preserving general linear methods of order p, stage order q=p or q=p−1, with r=p+1 external approximations, and s=p−1 internal approximations, for numerical solution of differential systems. Examples of methods of order p and stage order q=p or q=p−1, with large strong stability preserving coefficients and large regions of absolute stability, are provided for p=2, p=3, and p=4. The results of numerical experiments confirm that the methods constructed in this paper achieve the expected order of accuracy, do not produce spurious oscillations, and they are suitable to preserve the monotonicity of the numerical solution, when applied to discretization of hyperbolic conservation laws with discontinuous initial conditions.
KW - Construction of highly stable methods
KW - General linear methods
KW - Strong stability preserving (SSP)
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U2 - 10.1016/j.cam.2021.113612
DO - 10.1016/j.cam.2021.113612
M3 - Article
AN - SCOPUS:85105291699
SN - 0377-0427
VL - 396
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 113612
ER -