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Rare Permitted Matrix Solver

I want to solve a linear system in MatLab (corresponding to the PDE system of two equations written in a difference scheme). The action of the system matrix (corresponding to one of the diffusion terms of the PDE system) is read symbolically ( uis one of the unknown fields, nis a time step, jis a grid point):

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and completely:

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The above matrix should be denoted as A, where A * U ^ n + 1 = B is a system. ucontains 'u' and 'v' (second unknown field of the PDE system): U = [u_1, v_1, u_2, v_2, ..., u_J, v_J]. Until now, I filled this matrix, using spdiagsand diagfollowing expensive way:

    E=zeros(2*J,1);

    E(1:2:2*J) = 1;
    E(2:2:2*J) = 0;

    Dvec=zeros(2*J,1);

        for i=3:2:2*J-3
                 Dvec(i)=D_11((i+1)/2);    
        end

        for i=4:2:2*J-2
                 Dvec(i)=D_21(i/2);
        end

    A = diag(Dvec)*spdiags([-E,-E,2*E,2*E,-E,-E],[-3,-2,-1,0,1,2],2*J,2*J)/(dx^2);`

and to solve

[L,U]=lu(A);
 y = L\B; 
 U(:) =U\y;

where Bis the vector of the right side.

, JxJ, JxJ ..

: , MatLab , , Dvec , , D_11 D_22? !

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