function [H, HI, D1, D2, D4, e_l, e_r, M4, d2_l, d2_r, d3_l, d3_r, d1_l, d1_r] = d4_variable_8_higher_boundary_order(m,h)
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%% 8:te ordn. SBP Finita differens         %%%
    %%% operatorer med diagonal norm            %%%
    %%%                                         %%%
    %%%                                         %%%
    %%% H           (Normen)                    %%%
    %%% D1=H^(-1)Q  (approx f?rsta derivatan)   %%%
    %%% D2          (approx andra derivatan)    %%%
    %%% D2=HI*(R+C*D*S                          %%%
    %%%                                         %%%
    %%% R=-D1'*H*C*D1-RR                        %%%
    %%%                                         %%%
    %%% RR ?r dissipation)                      %%%
    %%% Dissipationen uppbyggd av D4:           %%%
    %%% DI=D4*B*H*D4                            %%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %This is 3rd order accurate at the boundary. Not same norm as D1 operator

    H = diag(ones(m,1),0);
    H(1:8,1:8) = [
        0.7488203e7/0.25401600e8 0 0 0 0 0 0 0;
        0 0.5539027e7/0.3628800e7 0 0 0 0 0 0;
        0 0 0.308923e6/0.1209600e7 0 0 0 0 0;
        0 0 0 0.1307491e7/0.725760e6 0 0 0 0;
        0 0 0 0 0.59407e5/0.145152e6 0 0 0;
        0 0 0 0 0 0.1548947e7/0.1209600e7 0 0;
        0 0 0 0 0 0 0.3347963e7/0.3628800e7 0;
        0 0 0 0 0 0 0 0.25641187e8/0.25401600e8;
    ];

    H(m-7:m,m-7:m) = fliplr(flipud(H(1:8,1:8)));

    e_1 = zeros(m,1);
    e_1(1) = 1;
    e_m = zeros(m,1);
    e_m(m) = 1;

    S_U = [-0.49e2/0.20e2 6 -0.15e2/0.2e1 0.20e2/0.3e1 -0.15e2/0.4e1 0.6e1/0.5e1 -0.1e1/0.6e1]/h;
    S_1 = zeros(1,m);
    S_1(1:7) = S_U;
    S_m = zeros(1,m);
    S_m(m-6:m) = fliplr(-S_U);

    S2_U = [0.203e3/0.45e2 -0.87e2/0.5e1 0.117e3/0.4e1 -0.254e3/0.9e1 0.33e2/0.2e1 -0.27e2/0.5e1 0.137e3/0.180e3]/h^2;
    S2_1 = zeros(1,m);
    S2_1(1:7) = S2_U;
    S2_m = zeros(1,m);
    S2_m(m-6:m) = fliplr(S2_U);

    S3_U = [-0.49e2/0.8e1 29 -0.461e3/0.8e1 62 -0.307e3/0.8e1 13 -0.15e2/0.8e1]/h^3;
    S3_1 = zeros(1,m);
    S3_1(1:7) = S3_U;
    S3_m = zeros(1,m);
    S3_m(m-6:m) = fliplr(-S3_U);

    H = h*H;
    HI = inv(H);

    % Fourth derivative, 1th order accurate at first 8 boundary points (still
    % yield 5th order convergence if stable: for example u_tt = -u_xxxx

    m5 = -0.41e2/0.7560e4;
    m4 =  0.1261e4/0.15120e5;
    m3 =  -0.541e3/0.840e3;
    m2 =  0.4369e4/0.1260e4;
    m1 =  -0.1669e4/0.180e3;
    m0 =  0.1529e4/0.120e3;

    M4 = m5*(diag(ones(m-5,1),5)+diag(ones(m-5,1),-5))+m4*(diag(ones(m-4,1),4)+diag(ones(m-4,1),-4))+m3*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3))+m2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2))+m1*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1))+m0*diag(ones(m,1),0);

    %M4 = (-1/6*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3) ) + 2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2)) -13/2*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1)) + 28/3*diag(ones(m,1),0));

    M4_U = [
        0.1031569831e10/0.155675520e9 -0.32874237931e11/0.1452971520e10 0.3069551773e10/0.90810720e8 -0.658395212131e12/0.21794572800e11 0.31068454007e11/0.1816214400e10 -0.39244130657e11/0.7264857600e10 0.1857767503e10/0.2724321600e10 0.1009939e7/0.49420800e8;
        -0.32874237931e11/0.1452971520e10 0.12799022387e11/0.155675520e9 -0.134456503627e12/0.1037836800e10 0.15366749479e11/0.129729600e9 -0.207640325549e12/0.3113510400e10 0.5396424073e10/0.259459200e9 -0.858079351e9/0.345945600e9 -0.19806607e8/0.170270100e9;
        0.3069551773e10/0.90810720e8 -0.134456503627e12/0.1037836800e10 0.6202056779e10/0.28828800e8 -0.210970327081e12/0.1037836800e10 0.2127730129e10/0.18532800e8 -0.4048692749e10/0.115315200e9 0.1025943959e10/0.259459200e9 0.71054663e8/0.290594304e9;
        -0.658395212131e12/0.21794572800e11 0.15366749479e11/0.129729600e9 -0.210970327081e12/0.1037836800e10 0.31025293213e11/0.155675520e9 -0.1147729001e10/0.9884160e7 0.1178067773e10/0.32432400e8 -0.13487255581e11/0.3113510400e10 -0.231082547e9/0.1816214400e10;
        0.31068454007e11/0.1816214400e10 -0.207640325549e12/0.3113510400e10 0.2127730129e10/0.18532800e8 -0.1147729001e10/0.9884160e7 0.11524865123e11/0.155675520e9 -0.29754506009e11/0.1037836800e10 0.14231221e8/0.2316600e7 -0.15030629699e11/0.21794572800e11;
        -0.39244130657e11/0.7264857600e10 0.5396424073e10/0.259459200e9 -0.4048692749e10/0.115315200e9 0.1178067773e10/0.32432400e8 -0.29754506009e11/0.1037836800e10 0.572247737e9/0.28828800e8 -0.11322059051e11/0.1037836800e10 0.3345834083e10/0.908107200e9;
        0.1857767503e10/0.2724321600e10 -0.858079351e9/0.345945600e9 0.1025943959e10/0.259459200e9 -0.13487255581e11/0.3113510400e10 0.14231221e8/0.2316600e7 -0.11322059051e11/0.1037836800e10 0.10478882597e11/0.778377600e9 -0.68446325191e11/0.7264857600e10;
        0.1009939e7/0.49420800e8 -0.19806607e8/0.170270100e9 0.71054663e8/0.290594304e9 -0.231082547e9/0.1816214400e10 -0.15030629699e11/0.21794572800e11 0.3345834083e10/0.908107200e9 -0.68446325191e11/0.7264857600e10 0.9944747557e10/0.778377600e9;
    ];

    M4(1:8,1:8) = M4_U;

    M4(m-7:m,m-7:m) = flipud( fliplr( M4_U ) );
    M4 = M4/h^3;

    D4 = HI*(M4-e_1*S3_1+e_m*S3_m  + S_1'*S2_1-S_m'*S2_m);
end