--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+sbp/+implementations/d2_variable_periodic_4.m	Thu Feb 08 16:44:46 2018 -0800
@@ -0,0 +1,57 @@
+function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_periodic_4(m,h)
+    % m = number of unique grid points, i.e. h = L/m;
+
+    if(m<5)
+        error(['Operator requires at least ' num2str(5) ' grid points']);
+    end
+
+    % Norm
+    Hv = ones(m,1);
+    Hv = h*Hv;
+    H = spdiag(Hv, 0);
+    HI = spdiag(1./Hv, 0);
+
+
+    % Dummy boundary operators
+    e_l = sparse(m,1);
+    e_r = rot90(e_l, 2);
+
+    d1_l = sparse(m,1);
+    d1_r = -rot90(d1_l, 2);
+
+    S = d1_l*d1_l' + d1_r*d1_r';
+
+    % D1 operator
+    stencil = [1/12 -2/3 0 2/3 -1/12];
+    diags = -2:2;
+    Q = stripeMatrixPeriodic(stencil, diags, m);
+    D1 = HI*(Q - 1/2*e_l*e_l' + 1/2*e_r*e_r');
+
+
+    scheme_width = 5;
+    scheme_radius = (scheme_width-1)/2;
+    
+    r = 1:m;
+    offset = scheme_width;
+    r = r + offset;
+
+    function D2 = D2_fun(c)
+        c = [c(end-scheme_width+1:end); c; c(1:scheme_width) ];
+
+        % Note: these coefficients are for -M.
+        Mm2 = -1/8*c(r-2) + 1/6*c(r-1) - 1/8*c(r);
+        Mm1 = 1/6 *c(r-2) + 1/2*c(r-1) + 1/2*c(r) + 1/6*c(r+1);
+        M0  = -1/24*c(r-2)- 5/6*c(r-1) - 3/4*c(r) - 5/6*c(r+1) - 1/24*c(r+2);
+        Mp1  = 0 * c(r-2) + 1/6*c(r-1) + 1/2*c(r) + 1/2*c(r+1) + 1/6 *c(r+2);
+        Mp2  = 0 * c(r-2) + 0 * c(r-1) - 1/8*c(r) + 1/6*c(r+1) - 1/8 *c(r+2);
+
+        vals = -[Mm2,Mm1,M0,Mp1,Mp2];
+        diags = -scheme_radius : scheme_radius;
+        M = spdiagsVariablePeriodic(vals,diags); 
+
+        M=M/h;
+        D2=HI*(-M );
+
+    end
+    D2 = @D2_fun;
+end
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