Beispiel - SAM - ETH Zürich

Listing 1.3: Numerische Integration des Lorenz-Systems
1 f u n c t i o n lorenzplot(rho,sigma,beta)
2
3 % MATLAB script for plotting 3D trajectories of the Lorenz system for
Ex. 1.3.36
4 % Arguments: parameters of the Lorenz system (1.3.37): ρ, σ, β.
5
6 % Default paramters
7 i f (nargin < 3), rho=28; sigma = 10; beta = 8/3; end
8
9 % function handle for right hand side of the Lorez system (1.3.37)
0 f = @(t,y) ([sigma*(y(2)-y(1));rho*y(1) - y(2) -
y(1)*y(3);y(1)*y(2) - beta*y(3)]);
1
2 y0 = [8 9 9.5]; ystart = y0; % initial conditions
3 ts = [0 20]; % Time for simulation
4
5 % Numerical integration of Lorenz system using MATLAB standard integrator,
6 % see Rem. 1.2.4
7 opts = odeset(’reltol’,1E-10,’abstol’,1E-10,’stats’,’on’);
8 [t,y] = ode45(f,ts,y0,opts);
9 y0(3) = y0(3) + 1.0E-5; % Slight perturbation of initial value
0 [tt,yt] = ode45(f,ts,y0,opts);
1
Numerische
Mathemtik
R. Hiptmair
rev 35327,
25. April
2011
1.3
p. 67