Beispiel - SAM - ETH Zürich

MATLAB-CODE : Berechnung des Präzession einer Magnetnadel
h = [-1;-1;-1]; tspan = [0 10000]; y0 = [0.5*sqrt(2);0;0.5*sqrt(2)];
fun = @(t,x) cross(x,h);
Jac = @(t,x) [0 h(3) -h(2); -h(3) 0 h(1); h(2) -h(1) 0];
options = odeset(’reltol’,0.001,’abstol’,1e-4,’stats’,’on’);
[t45,y45] = ode45(fun,tspan,y0,options);
options = odeset(’reltol’,0.001,’abstol’,1e-4,’stats’,’on’,’Jacobian’,Jac);
[t23,y23] = ode23s(fun,tspan,y0,options);
Numerische
Mathemtik
ode45: 24537 successful steps, 7432 failed attempts, 191815 function evaluations
ode23s: 93447 successful steps, 4632 failed attempts, 289607 function evaluations
1.1
1.05
ode45
oed23s
R. Hiptmair
rev 35327,
24. Juni
2011
1
1
y 3
0.5
0
y(t)
ode45
ode23s
Laenge |y(t)|
0.95
0.9
−0.5
1
0.5
0
y 1
−0.5
1
0.5
y 2
0
−0.5
Fig. 149
0.85
0.8
0.75
0 2000 4000 6000 8000 10000
t
Fig. 150
4.1
p. 437