TY - JOUR
T1 - Nonautonomous stability of linear multistep methods
AU - Boutelje, B R
AU - Hill, Adrian T
PY - 2010/4
Y1 - 2010/4
N2 - A linear scalar nonautonomous initial-value problem (IVP) is governed by a scalar lambda(t) with a nonpositive real part. For a wide class of linear multistep methods, including BDF4-6, it is shown that negative real lambda(t) may be chosen to generate instability in the method when applied to the IVP. However, a uniform-in-time stability result holds when lambda(.) is a Lipschitz function, subject to a related restriction on h. The proof involves the construction of a Lyapunov function based on a convex combination of G-norms.
AB - A linear scalar nonautonomous initial-value problem (IVP) is governed by a scalar lambda(t) with a nonpositive real part. For a wide class of linear multistep methods, including BDF4-6, it is shown that negative real lambda(t) may be chosen to generate instability in the method when applied to the IVP. However, a uniform-in-time stability result holds when lambda(.) is a Lipschitz function, subject to a related restriction on h. The proof involves the construction of a Lyapunov function based on a convex combination of G-norms.
UR - http://www.scopus.com/inward/record.url?scp=77950295776&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1093/imanum/drn070
U2 - 10.1093/imanum/drn070
DO - 10.1093/imanum/drn070
M3 - Article
SN - 0272-4979
VL - 30
SP - 525
EP - 542
JO - IMA Journal of Numerical Analysis
JF - IMA Journal of Numerical Analysis
IS - 2
ER -