%alpha=0.5;
%x=linspace(0,1,N);
ysteady=(1+1/2/alpha/alpha)*x-x.*x/2/alpha/alpha;
yext=[ysteady -ysteady(N-1:-1:2)]; % length(yext)=2*(N-1)
yext(N)=0; % the midpoint of the discontinuity
k=pi*[0:N-1 -(N-2):-1]; %2*(N-1) frequencies
fftyext=fft(yext);
ytransient=-real(ifft(exp(-alpha*alpha*k.*k*t).*fftyext));
yt=ysteady+ytransient(1:N);
%plot(x,yt)