Beispiel - SAM - ETH Zürich

k i =f(y 0 )+hDf(y 0 )
⎛
1
2
h 2 D 2 f(y 0 ) ⎝
=f(y 0 )+h
s∑
j=1
a ij
⎛
⎝f ( y 0 +hDf(y 0 )
s∑
a ij (f(y 0 )+O(h)),
j=1
·∑s
j=1 a ij
} {{ }
=c i , siehe Bem. 2.3.15
⎞
s∑
a il k l +O(h 2 ) ) ⎠+
l=1
⎞
s∑
a ij (f(y 0 )+O(h)) ⎠+O(h 3 )
j=1
Df(y 0 )f(y 0 )+
h 2( ∑ s )
a il c l Df(y0 )Df(y 0 )f(y 0 )+h 21 2 c2 i D2 f(y 0 )(f(y 0 ),f(y 0 ))+O(h 3 ) .
l=1
Numerische
Mathemtik
R. Hiptmair
rev 35327,
25. April
2011
2.3
p. 242