Research in Scientific Computation - SERC
Research in Scientific Computation - SERC
Research in Scientific Computation - SERC
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The Stochastic alpha Method<br />
x n1<br />
=x n<br />
v n<br />
h1−2 n<br />
2 n1<br />
h 2<br />
m<br />
2 B n I .,0 ∑ k =1<br />
v n1<br />
=v n<br />
1− n<br />
n1<br />
hB n<br />
W n1<br />
−W n<br />
∑ k =1<br />
m<br />
n1<br />
= m<br />
−1 n<br />
1− f<br />
f n<br />
f<br />
f n1<br />
.<br />
n<br />
∑ i=1<br />
B i , l ∂ B : ,k<br />
m = 2 −1<br />
1<br />
∂ v i<br />
n<br />
=: C<br />
1B<br />
l , k<br />
f = 1<br />
n<br />
B :={b j }<br />
=<br />
=<br />
, determ<strong>in</strong>ed from stability requirement<br />
m<br />
m<br />
∑ l =1<br />
m<br />
∑ l=1<br />
C<br />
1B<br />
l , k n I l , k , 0<br />
C<br />
1B<br />
l , k n I l , k
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