n=48;T=1;k=T/n;
t=linspace(0,T,n+1);
u=zeros(1,n+1);
u(1)=1;
for i=1:n
    if 4*k*u(i)>1
        break
    else
        u(i+1)=1/(2*k)*(1-sqrt(1-4*k*u(i)));
    end
end
plot(t,u)