Beispiel - SAM - ETH Zürich

6
7 % Stoermer-Verlet iteration
8 y_sv = y0; y_sv = [y_sv,y_new]; y_p = v0;
9 f o r k=2:N+1
0 y = -y_old + 2*y_new + h*h*f(y_new);
1 y_p = [y_p,(y-y_old)/(2*h)];
2 y_old = y_new; y_new = y;
3 y_sv = [y_sv,y];
4 end
5 y_sv = y_sv(1:end-1);
6
7 % right hand side (Hamiltonian form) for computation of reference solution
8 % with high-order single step method with tight tolerances
9 odefun = @(t,y) [y(2);-g/l*sin(y(1))];
0 [t,y] = ode45(odefun,[0,T],[y0;v0],...
1 odeset(’abstol’,1E-11,’reltol’,1E-11,’stats’,’on’));
2
3 % Plot of angle vs. time
4 f i g u r e(’name’,’Pendulum alpha’);
5 p l o t(t,y(:,1),’g-’,h*(0:N),y_sv,’r-+’);
6 x l a b e l(’{\bf time t}’,’fontsize’,14);
7 y l a b e l(’{\bf angle \alpha}’,’fontsize’,14);
8 t i t l e( s p r i n t f(’Pendulum g = %f, l =
Numerische
Mathemtik
R. Hiptmair
rev 35327,
25. April
2011
1.4
p. 108