TY - JOUR
T1 - The stability problem for linear multistep methods: old and new results
AU - ACETO, LIDIA
AU - TRIGIANTE, D.
N1 - Funding Information:
Supported by Italian M.I.U.R.
PY - 2007
Y1 - 2007
N2 - The paper reviews results on rigorous proofs for stability properties of classes of linear multistep methods (LMMs) used either as IVMs or as BVMs. The considered classes are not only the well-known classical ones (BDF, Adams, ...) along with their BVM correspondent, but also those which were considered unstable as IVMs, but stable as BVMs. Among the latter we find two classes which deserve attention because of their peculiarity: the TOMs (top order methods) which have the highest order allowed to a LMM and the Bs-LMMs which have the property to carry with each method its natural continuous extension.
AB - The paper reviews results on rigorous proofs for stability properties of classes of linear multistep methods (LMMs) used either as IVMs or as BVMs. The considered classes are not only the well-known classical ones (BDF, Adams, ...) along with their BVM correspondent, but also those which were considered unstable as IVMs, but stable as BVMs. Among the latter we find two classes which deserve attention because of their peculiarity: the TOMs (top order methods) which have the highest order allowed to a LMM and the Bs-LMMs which have the property to carry with each method its natural continuous extension.
KW - Boundary value methods
KW - Linear multistep methods
KW - Stability
KW - Boundary value methods
KW - Linear multistep methods
KW - Stability
UR - https://iris.uniupo.it/handle/11579/126611
U2 - 10.1016/j.cam.2006.10.052
DO - 10.1016/j.cam.2006.10.052
M3 - Article
SN - 0377-0427
VL - 210
SP - 2
EP - 12
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1-2
ER -