Lotka-Volterramodellen - Home Page of Lars Holm Jensen
Lotka-Volterramodellen - Home Page of Lars Holm Jensen
Lotka-Volterramodellen - Home Page of Lars Holm Jensen
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1 = b0 + ∆t kb11 + 2(kb12 + kb13) + kb14<br />
6<br />
0, 36 + 2(0, 3597 + 0, 3597) + 0, 3594<br />
= 1, 2 + 0, 01 · = 1, 2036<br />
6<br />
r1 = b0 + ∆t kr11 + 2(kr12 + kr13) + kr14<br />
6<br />
0, 14 + 2(0, 1414 + 0, 1414) + 0, 1428<br />
= 0.7 + 0, 01 · = 0, 7014<br />
6<br />
Iteration 2:<br />
Nu bestemmes værdierne kb21 . . . kb24 og kr21 . . . kr24:<br />
kb21 = f(t0, b0) = (A − Br0)b0 = (1 − 1 · 0.7014)1, 2036 = 0.3594<br />
kr21 = f(t0, b0) = (Cb0 − D)r0 = (1 · 1, 2036 − 1)0, 7014 = 0, 1428<br />
kb22 =<br />
<br />
f t0 + ∆t<br />
2 , b0 + ∆t<br />
2 kb21<br />
<br />
= (A − Br0)(b0 + ∆t<br />
2 kb21)<br />
=<br />
0, 01<br />
(1 − 1 · 0, 7014)(1, 2036 + · 0, 3594) = 0, 3591<br />
2<br />
kr22 =<br />
<br />
f t0 + ∆t<br />
2 , r0 + ∆t<br />
2 kr21<br />
<br />
= (Cb0 − D)(r0 + ∆t<br />
2 kr21)<br />
= (1 · 1, 2036 − 1)(0, 7014 +<br />
0, 01<br />
2<br />
· 0, 1428) = 0, 1442<br />
kb23 =<br />
<br />
f t0 + ∆t<br />
2 , b0 + ∆t<br />
2 kb22<br />
<br />
= (A − Br0)(b0 + ∆t<br />
2 kb22)<br />
=<br />
0, 01<br />
(1 − 1 · 0, 7014)(1, 2036 + · 0, 3591) = 0, 3590<br />
2<br />
kr23 =<br />
<br />
f t0 + ∆t<br />
2 , r0 + ∆t<br />
2 kr22<br />
<br />
= (Cb0 − D)(r0 + ∆t<br />
2 kr22)<br />
= (1 · 1, 2036 − 1)(0, 7014 +<br />
0, 01<br />
2<br />
· 0, 1442) = 0, 1442<br />
kb24 = f (t0 + ∆, x0 + ∆t · kb23) = (A − Br0)(b0 + ∆t · kb23)<br />
= (1 − 1 · 0, 7014)(1, 2036 + 0, 01 ∗ 0, 3590) = 0, 3587<br />
kr24 = f (t0 + ∆t, x0 + ∆t · kr23) = (Cb0 − D)(r0 + ∆t · kr23)<br />
= (1 · 1, 2036 − 1)(0, 7014 + 0, 01 · 0, 1442) = 0, 1456