Gunilla Kreiss: Differentialekvationer som matematiska ... - Skolverket
Gunilla Kreiss: Differentialekvationer som matematiska ... - Skolverket
Gunilla Kreiss: Differentialekvationer som matematiska ... - Skolverket
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! @ UU/IT<br />
p ij n+1 "2 pij n +pij n"1<br />
(c#t) 2<br />
UU/IT<br />
Partiella differentialekvationer:<br />
y<br />
Ljudutbredning<br />
x<br />
= p n n n<br />
i+1j "2 pij+pi"1j #x 2<br />
!<br />
Diskretisera<br />
xi = i"x,<br />
y j = j"y,<br />
t n = n"t,<br />
n<br />
pi, j # p(xi , y j ,tn )<br />
+ p n n n<br />
ij+1"2<br />
pij+pij+1 #y 2<br />
5/14/12 | #25
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