f=inline('y+t','t','y');h=1;
h_vect=[];err_vect=[];
eul_vect=[];rk2_vect=[];rk4_vect=[];
t=0:.05:3;
y=-t-1+2*exp(t);
for k=1:8
[teuler,yeuler]=eul(f,[0,3],1,h);
[trk2,yrk2]=rk2(f,[0,3],1,h);
[trk4,yrk4]=rk4(f,[0,3],1,h);
plot(t,y,teuler,yeuler,'o',trk2,yrk2,'+',trk4,yrk4,'*')
legend('Exact','Euler', 'RK2','RK4')
shg
zeuler=-1-teuler+2*exp(teuler);
eulerror=max(abs(zeuler-yeuler));
zrk2=-1-trk2+2*exp(trk2);
rk2error=max(abs(zrk2-yrk2));
zrk4=-1-trk4+2*exp(trk4);
rk4error=max(abs(zrk4-yrk4));
h_vect=[h_vect,h]
eul_vect=[eul_vect,eulerror]
rk2_vect=[rk2_vect,rk2error]
rk4_vect=[rk4_vect,rk4error]
pause
h=h/2;
end
loglog(h_vect,eul_vect,h_vect,rk2_vect,h_vect,rk4_vect)
legend('eul','rk2','rk4',4)
xlabel('Step size'), ylabel('Maximum error')
title('Maximum error vs. step size'), axis tight