Introduction to Scientific Computing - Tutorial 13: Recapitulation
Introduction to Scientific Computing - Tutorial 13: Recapitulation
Introduction to Scientific Computing - Tutorial 13: Recapitulation
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Consistency<br />
Write numerical method for ODE<br />
in a form:<br />
1<br />
h<br />
ẋ = f (t, x)<br />
k∑<br />
x n+k−i = ϕ f (t, x n+k , ..., x n , h)<br />
i=0<br />
Then find characteristic polynomial ρ(ξ) when ϕ f = 0 and its roots<br />
ξ. Then the method is consistent if<br />
and<br />
is equal <strong>to</strong> function f .<br />
ρ(1) = 0<br />
ϕ f (t, x, x, .., x, o)<br />
ρ ′ (1)<br />
1. Februar 20<strong>13</strong> Bojana Rosic <strong>Introduction</strong> <strong>to</strong> <strong>Scientific</strong> <strong>Computing</strong> Seite 11
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