TY - JOUR
T1 - Unconditionally stable general linear methods for ordinary differential equations
AU - Butcher, J. C.
AU - Jackiewicz, Zdzislaw
N1 - Funding Information:
★ Received December 2003. Accepted April 2004. Communicated by Timo Eirola. ★★ The work of this author was assisted by the Marsden Fund of New Zealand. † The work of this author was partially supported by the National Science Foundation under grant NSF DMS-9971164.
PY - 2004/8
Y1 - 2004/8
N2 - We describe a new approach to the construction of general linear methods with inherent Runge-Kutta stability properties, which are unconditionally stable for any stepsize pattern. These methods permit an accurate, efficient and reliable estimation of the local discretization errors. This is confirmed by numerical experiments.
AB - We describe a new approach to the construction of general linear methods with inherent Runge-Kutta stability properties, which are unconditionally stable for any stepsize pattern. These methods permit an accurate, efficient and reliable estimation of the local discretization errors. This is confirmed by numerical experiments.
KW - general linear methods
KW - inherent Runge-Kutta stability
KW - unconditional stability
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U2 - 10.1023/B:BITN.0000046804.67936.06
DO - 10.1023/B:BITN.0000046804.67936.06
M3 - Article
AN - SCOPUS:8144230572
SN - 0006-3835
VL - 44
SP - 557
EP - 570
JO - BIT Numerical Mathematics
JF - BIT Numerical Mathematics
IS - 3
ER -