function euler_method2

nn=5;                %initial number of subintervals
k=5;                 %number of approximations   
for m=1:k
    n=nn*2^(m-1);    %number of subintervals
    e=zeros(n+1);
    h=5/n;           %step size
    t=0:h:5;
    for i=1:n
        %e(i+1)=e(i)+h*subs(f,x,e(i));
        e(i+1)=e(i)+h*f(h*i,e(i)); %carrying out Euler method
    end
    y=exact(t);
    %y=subs(exact,x,t);
    error(m)=abs(y(n+1)-e(n+1));%error at t=5
    plot(t,e);
    hold on;
end


plot(t,y,'r');
error
for m=1:k-1
    ratio(m)=error(m)/error(m+1);
end
ratio

function d=f(t,x)
d=-1/2*exp(t/2)*sin(5*t)+5*exp(t/2)*cos(5*t)+x;

function d=exact(x)
d=exp(x/2).*sin(5*x);