TY - JOUR
T1 - A new class of efficient general linear methods for ordinary differential equations
AU - Braś, M.
AU - Jackiewicz, Z.
N1 - Funding Information:
The work of the first author (M. Braś) was partially supported by the Faculty of Applied Mathematics AGH UST statutory tasks within subsidy of Ministry of Science and Higher Education .
Publisher Copyright:
© 2020 IMACS
PY - 2020/5
Y1 - 2020/5
N2 - We describe the construction of a new class of efficient general linear methods of high stage order, for nonstiff and stiff differential systems. Examples of explicit methods with large regions of stability, and implicit methods which are A- and L-stable, up to the order p=4 are presented. It is confirmed by numerical experiments that all methods achieve the expected order of accuracy and no order reduction occurs for stiff systems.
AB - We describe the construction of a new class of efficient general linear methods of high stage order, for nonstiff and stiff differential systems. Examples of explicit methods with large regions of stability, and implicit methods which are A- and L-stable, up to the order p=4 are presented. It is confirmed by numerical experiments that all methods achieve the expected order of accuracy and no order reduction occurs for stiff systems.
KW - Continuous extensions
KW - General linear methods
KW - Local discretization errors
KW - Stability analysis
KW - Stage order and order conditions
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U2 - 10.1016/j.apnum.2019.12.022
DO - 10.1016/j.apnum.2019.12.022
M3 - Article
AN - SCOPUS:85077741280
SN - 0168-9274
VL - 151
SP - 282
EP - 300
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -