Beispiel - SAM - ETH Zürich

5 % tspan = [t0 T]: initial and final time
6 % y0v ˆ= array of initial values
7 % N ˆ= vector containing numbers of steps. For each the error is returned
8
9 err = []; l = 1; % Initialize error array
0
1 f o r y0 = y0v
2 % Compute ’exact’ solution
3 [t,y] =
ode45(odefun,tspan,y0,odeset(’reltol’,1E-11,’abstol’,1E-11));
4
5 % Compute Euler solutions
6 erri = [];
7 f o r n=N
8 h = (tspan(2)-tspan(1))/n; % uniform timestep size
9 t_eul = tspan(1); % initial time
0 y_eul = y0; % intialize iteration
1 f o r k=1:n
2 y_eul = y_eul + h*odefun(t_eul,y_eul); % see (1.4.2)
3 t_eul = t_eul + h; % increment time
4 end
5 erri = [erri,norm(y(end,:)-y_eul)]; % record error
6 end
Numerische
Mathemtik
R. Hiptmair
rev 35327,
25. April
2011
1.4
p. 76