function [x, Dx, Dxx] = diffper(n, xspan)
%DIFFPER   Differentiation matrices for periodic conditions. 
% Input:
%   n      number of subintervals (integer)
%   xspan  endpoints of domain (vector)
% Output:
%   x    equispaced nodes (length n)
%   Dx   matrix for first derivative (n by n)
%   Dxx  matrix for second derivative (n by n)

    a = xspan(1);  
    b = xspan(2);
    h = (b-a)/n;
    x = a + h*(0:n-1)';   % nodes, omitting the repeated data

    % Construct Dx by diagonals, then correct the corners.
    dp = 0.5*ones(n-1,1)/h;      % superdiagonal
    dm = -0.5*ones(n-1,1)/h;     % subdiagonal
    Dx = diag(dm,-1) + diag(dp,1);
    Dx(1,n) = -1/(2*h);
    Dx(n,1) = 1/(2*h);

    % Construct Dxx by diagonals, then correct the corners.
    d0 =  -2*ones(n,1)/h^2;      % main diagonal
    dp =  ones(n-1,1)/h^2;       % superdiagonal
    dm =  dp;                    % subdiagonal
    Dxx = diag(dm,-1) + diag(d0) + diag(dp,1);
    Dxx(1,n) = 1/(h^2);
    Dxx(n,1) = 1/(h^2);

end