Institut für Allgemeine Elektrotechnik, Uni Rostock - Universität ...

Stability
Stability is one of the most important properties of a numerical
integration scheme.
( Δt)
The linear recursion operator G depends on Δt.
Several slightly different definitions can be found for the term "stability" ,
the following plays an important role in convergence analysis.
Definition by Lax-Richtmeyer:
( m+
)
Δ
(
t0
>
) ( m
t
) 1
( t)
Prof. Dr. Ursula van Rienen, Universität Rostock, Fakultät für Informatik und Elektrotechnik (IEF), Institut für Allgemeine Elektrotechnik (IAE)
( m)
A recursion y = G Δ y is stable
if a constant C and
a value 0 exist for each (fixed) value T such that
holds.
( ) ( m)
G Δ ≤C
∀m⋅Δt ≤T and Δt < Δt
i.e. G Δt remains bounded for Δt →0 and constant T ( m →∞).
0
13