Beispiel - SAM - ETH Zürich

2 % Ricatti differential equation for Example 1.1.3
3 f u n c t i o n Ricatti
4
5 % define the right hand side of the differential equation as function handle
6 fn = @(t,x) x.^2+t^2;
7
8 % plot solution curves
9 f i g u r e(’Name’,’Ricatti’); hold on;
0 % run ode45 and plot resuts for different starting values on y-axis
1 f o r v = 0.05:0.1:1.4
2 [t,y] = ode45(fn,[0 1.5],v);
3 p l o t(t,y,’r-’);
4 end
5 % run ode45 and plot resuts for different starting values on x-axis
6 f o r v = [0.4 0.7 1.0 1.2 1.4]
7 [t,y] = ode45(fn,[v 1.5],0);
8 p l o t(t,y,’r-’);
9 end
0 % set axes, labels, ...
1 set(gca,’fontsize’,14); axis([0 1.5 0 1.5]);
2 x l a b e l(’{\bf t}’); y l a b e l(’{\bf y}’);
3 % Create EPS output file
4 p r i n t -depsc2 ’riccatti1.eps’
Numerische
Mathemtik
R. Hiptmair
rev 35327,
25. April
2011
1.1
p. 16