f = @(t,y) [y(2);-y(1)];
tspan = [0,40];
yinit = [1;0];
h1 = 0.1;
h2 = 1;

clf;
[Y,T] = expMPR(f,tspan,yinit,h1);
figure(1);
plot(T,Y);
titel1 = sprintf('Schrittweite: %f',h1);
title(titel1);

[Y1,T1] = expMPR(f,tspan,yinit,h2);
figure(2);
plot(T1,Y1);
titel2 = sprintf('Schrittweite: %f',h2);
title(titel2);

figure(3)
plot(T,Y(1,:),'b',T,Y(2,:),'k',T1,Y1(1,:),'m',T1,Y1(2,:),'r');
legend('u','v','u','v');



% Matlab-eigene Integratoren

% Explizites Runge-Kutta Verfahren
[T,Y] = ode45(f, tspan, yinit);
figure(4);
plot(T, Y);

% BDF-Verfahren
[T,Y] = ode15s(f, tspan, yinit);
figure(5);
plot(T, Y);
