--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+sbp/+implementations/d2_variable_periodic_8.m	Fri May 13 13:28:10 2022 +0200
@@ -0,0 +1,75 @@
+function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_periodic_8(m,h)
+    % m = number of unique grid points, i.e. h = L/m;
+
+    if(m<9)
+        error(['Operator requires at least ' num2str(8) ' 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);
+
+
+    % D1 operator
+    diags   = -4:4;
+    stencil = [1/280, -4/105, 1/5, -4/5, 0, 4/5, -1/5, 4/105, -1/280];
+    D1 = stripeMatrixPeriodic(stencil, diags, m);
+    D1 = D1/h;
+
+    % Undivided differences
+    diags   = -3:2;
+    stencil = [-1 5 -10 10 -5 1];
+    DD_5 = stripeMatrixPeriodic(stencil, diags, m);
+
+    diags   = -3:3;
+    stencil = [1 -6 15 -20 15 -6 1];
+    DD_6 = stripeMatrixPeriodic(stencil, diags, m);
+
+    diags   = -4:3;
+    stencil = [-1 7 -21 35 -35 21 -7 1];
+    DD_7 = stripeMatrixPeriodic(stencil, diags, m);
+
+    diags   = -4:4;
+    stencil = [1 -8 28 -56 70 -56 28 -8 1];
+    DD_8 = stripeMatrixPeriodic(stencil, diags, m);
+
+    % D2 operator
+    function D2 = D2_fun(c)
+
+        C1 = sparse(diag(c));
+        
+        diags   = -1:0;
+        stencil = [1/2, 1/2];
+        C2 = stripeMatrixPeriodic(stencil, diags, m);
+
+        diags   = -1:1;
+        stencil = [3/10, 2/5, 3/10];
+        C3 = stripeMatrixPeriodic(stencil, diags, m);
+
+        diags   = -2:1;
+        stencil = [1/4, 1/4, 1/4, 1/4];
+        C4 = stripeMatrixPeriodic(stencil, diags, m);
+
+        C2 = sparse(diag(C2 * c));
+        C3 = sparse(diag(C3 * c));
+        C4 = sparse(diag(C4 * c));
+
+        % Remainder term added to wide second derivative operator
+        R = (1/78400 / h) * transpose(DD_8) * C1 * DD_8 + (1/14700 / h) * transpose(DD_7) * C2 * DD_7 + (1/2520 / h) * transpose(DD_6) * C3 * DD_6 + (1/350 / h) * transpose(DD_5) * C4 * DD_5;
+
+        D2 = D1 * C1 * D1 - H \ R;
+    end
+    D2 = @D2_fun;
+
+
+end