Introduction to Scientific Computing - Tutorial 13: Recapitulation

Stability of linear multistep method
and
σ(ξ) := hλ
k∑
β j x j
characteristic polynomial for RHS ∑ k
j=0 β jf n+j = 0. Then stability is
determined by roots
ρ(ξ) − zσ(ξ) = 0
i.e. region:
G s := {z ∈ C : |ξ l | 1and if ξ l is multiple root then |ξ l | < 1}
j=0
1. Februar 2013 Bojana Rosic Introduction to Scientific Computing Seite 16