TY - JOUR
T1 - Search for efficient general linear methods for ordinary differential equations
AU - Braś, M.
AU - Jackiewicz, Zdzislaw
N1 - Funding Information:
The work of the first author was supported by the National Science Center under grant DEC-2011/01/N/ST1/02672 and by the Polish Ministry of Science and Higher Education .
PY - 2014/5/15
Y1 - 2014/5/15
N2 - We analyze implicit general linear methods with s internal stages and r=s+1 external stages of order p=s+1 and stage order q=s or q=s+1. These methods might eventually lead to more efficient formulas than the class of DIMSIMs and the class of general linear methods with inherent Runge-Kutta stability. We analyze also error propagation and estimation of local discretization errors. Examples of such methods which are A- and L-stable are derived up to the stage order q=3 or q=4 and order p=4.
AB - We analyze implicit general linear methods with s internal stages and r=s+1 external stages of order p=s+1 and stage order q=s or q=s+1. These methods might eventually lead to more efficient formulas than the class of DIMSIMs and the class of general linear methods with inherent Runge-Kutta stability. We analyze also error propagation and estimation of local discretization errors. Examples of such methods which are A- and L-stable are derived up to the stage order q=3 or q=4 and order p=4.
KW - A- and L-stability
KW - Construction of highly stable methods
KW - Error propagation
KW - General linear methods
KW - Order and stage order
KW - Order conditions
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U2 - 10.1016/j.cam.2013.07.032
DO - 10.1016/j.cam.2013.07.032
M3 - Article
AN - SCOPUS:84893818153
SN - 0377-0427
VL - 262
SP - 180
EP - 192
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -