TY - JOUR
T1 - Strong Stability Preserving General Linear Methods with Runge–Kutta Stability
AU - Califano, Giovanna
AU - Izzo, Giuseppe
AU - Jackiewicz, Zdzislaw
N1 - Funding Information:
Giovanna Califano: The work of this author was supported by an UNISA research Grant. Giuseppe Izzo: The work of this author was partially supported by GNCS-INdAM.
Funding Information:
The research reported in this paper was started during the visit of the first author (GC) to Arizona State University in the Spring semester of 2017. This author wish to express her gratitude to the School of Mathematical and Statistical Sciences for hospitality during this visit. We would also like to express our gratitude to anonymous referees whose comments helped us to improve the presentation of this paper. Giovanna Califano: The work of this author was supported by an UNISA research Grant. Giuseppe Izzo: The work of this author was partially supported by GNCS-INdAM.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - We investigate strong stability preserving (SSP) general linear methods (GLMs) for systems of ordinary differential equations. Such methods are obtained by the solution of the minimization problems with nonlinear inequality constrains, corresponding to the SSP property of these methods, and equality constrains, corresponding to order and stage order conditions. These minimization problems were solved by the sequential quadratic programming algorithm implemented in MATLAB® subroutine fmincon.m starting with many random guesses. Examples of transformed SSP GLMs of order p= 1 , 2 , 3 , and 4, and stage order q= p have been determined, and suitable starting and finishing procedures have been constructed. The numerical experiments performed on a set of test problems have shown that transformed SSP GLMs constructed in this paper are more accurate than transformed SSP DIMSIMs and SSP Runge–Kutta methods of the same order.
AB - We investigate strong stability preserving (SSP) general linear methods (GLMs) for systems of ordinary differential equations. Such methods are obtained by the solution of the minimization problems with nonlinear inequality constrains, corresponding to the SSP property of these methods, and equality constrains, corresponding to order and stage order conditions. These minimization problems were solved by the sequential quadratic programming algorithm implemented in MATLAB® subroutine fmincon.m starting with many random guesses. Examples of transformed SSP GLMs of order p= 1 , 2 , 3 , and 4, and stage order q= p have been determined, and suitable starting and finishing procedures have been constructed. The numerical experiments performed on a set of test problems have shown that transformed SSP GLMs constructed in this paper are more accurate than transformed SSP DIMSIMs and SSP Runge–Kutta methods of the same order.
KW - Construction of SSP methods
KW - General linear methods
KW - Inherent Runge–Kutta stability
KW - Order conditions
KW - Runge–Kutta stability
KW - Strong stability preserving (SSP) methods
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U2 - 10.1007/s10915-018-0646-5
DO - 10.1007/s10915-018-0646-5
M3 - Article
AN - SCOPUS:85040780990
SN - 0885-7474
VL - 76
SP - 943
EP - 968
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 2
ER -