Institut für Allgemeine Elektrotechnik, Uni Rostock - Universität ...
Institut für Allgemeine Elektrotechnik, Uni Rostock - Universität ...
Institut für Allgemeine Elektrotechnik, Uni Rostock - Universität ...
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Central Difference Quotient (Leap Frog)<br />
⎛ 2 1 1 1<br />
Inserting the estimate ωmax<br />
≤ max = max<br />
+ +<br />
⎜<br />
⎝ ε u v w<br />
iµ<br />
Δ Δ Δ<br />
i<br />
for the absolute largest eigenvalue yields again<br />
⎧<br />
⎫<br />
1<br />
⎪<br />
⎪<br />
Δt ≤Δt max<br />
≈min ⎨ εi µ<br />
i<br />
⋅<br />
,<br />
i<br />
1 1 1<br />
⎬<br />
⎪<br />
+ + ⎪<br />
2 2 2<br />
⎪⎩<br />
Δui Δvi Δwi<br />
⎪⎭<br />
i.e. the Courant-Friedrichs-Levy condition.<br />
( ωi<br />
) ⎜<br />
2 2 2<br />
i i i<br />
⎞<br />
⎟<br />
⎠<br />
ω<br />
max<br />
can also be determined numerically, yielding an<br />
exact stability limit for the leap-frog scheme.<br />
Prof. Dr. Ursula van Rienen, <strong>Uni</strong>versität <strong>Rostock</strong>, Fakultät <strong>für</strong> Informatik und <strong>Elektrotechnik</strong> (IEF), <strong>Institut</strong> <strong>für</strong> <strong>Allgemeine</strong> <strong>Elektrotechnik</strong> (IAE)<br />
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