TY - JOUR
T1 - Extrapolation-based implicit-explicit general linear methods
AU - Cardone, Angelamaria
AU - Jackiewicz, Zdzislaw
AU - Sandu, Adrian
AU - Zhang, Hong
N1 - Funding Information:
Acknowledgments The results reported in this paper were obtained during the visit of the first author to the Arizona State University in January–May of 2013. This author wish to express her gratitude to the School of Mathematical and Statistical Sciences for hospitality during this visit. The work of Sandu and Zhang has been supported in part by the awards NSF OCI-8670904397, NSF CCF-0916493, NSF DMS-0915047, NSF CMMI-1130667, NSF CCF-1218454, AFOSR FA9550-12-1-0293-DEF, AFOSR 12-2640-06, and by the Computational Science Laboratory at Virginia Tech.
PY - 2014/3
Y1 - 2014/3
N2 - For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems implicit-explicit (IMEX) integration combines an explicit scheme for the non-stiff part with an implicit scheme for the stiff part. In a recent series of papers two of the authors (Sandu and Zhang) have developed IMEX GLMs, a family of implicit-explicit schemes based on general linear methods. It has been shown that, due to their high stage order, IMEX GLMs require no additional coupling order conditions, and are not marred by order reduction. This work develops a new extrapolation-based approach to construct practical IMEX GLM pairs of high order. We look for methods with large absolute stability region, assuming that the implicit part of the method is A- or L-stable. We provide examples of IMEX GLMs with optimal stability properties. Their application to a two dimensional test problem confirms the theoretical findings.
AB - For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems implicit-explicit (IMEX) integration combines an explicit scheme for the non-stiff part with an implicit scheme for the stiff part. In a recent series of papers two of the authors (Sandu and Zhang) have developed IMEX GLMs, a family of implicit-explicit schemes based on general linear methods. It has been shown that, due to their high stage order, IMEX GLMs require no additional coupling order conditions, and are not marred by order reduction. This work develops a new extrapolation-based approach to construct practical IMEX GLM pairs of high order. We look for methods with large absolute stability region, assuming that the implicit part of the method is A- or L-stable. We provide examples of IMEX GLMs with optimal stability properties. Their application to a two dimensional test problem confirms the theoretical findings.
KW - Error analysis
KW - General linear methods
KW - IMEX methods
KW - Order conditions
KW - Stability analysis
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U2 - 10.1007/s11075-013-9759-y
DO - 10.1007/s11075-013-9759-y
M3 - Article
AN - SCOPUS:84897608836
SN - 1017-1398
VL - 65
SP - 377
EP - 399
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 3
ER -