function [grad_l, grad_r] = eno2y(m,n,i,j,phi,dy)

% phi(m+1,n+1), the level set function, m,n>=3.

    dydy = dy*dy;

    if j > 1
      phy_l = (phi(i,j) - phi(i,j-1) )/dy;
    else
      phi_l = 3*phi(i,j) - 3*phi(i,j+1) + phi(i,j+2);
      phy_l = (phi(i,j) - phi_l )/dy;
    end

    if j < n+1
      phy_r = (phi(i,j+1) - phi(i,j) )/dy;
    else
      phi_r = 3*phi(i,j) - 3*phi(i,j-1) + phi(i,j-2);      
      phy_r = (phi_r - phi(i,j) )/dy;
    end

    if j > 1
      if j==2
        phi_l = 3*phi(i,j-1) - 3*phi(i,j) + phi(i,j+1);
	phyy_l = (phi(i,j) - 2*phi(i,j-1) + phi_l )/dydy;
      else
        phyy_l = (phi(i,j) - 2*phi(i,j-1) + phi(i,j-2) )/dydy;
      end
    else
      phi_l = 3*phi(i,j) - 3*phi(i,j+1) + phi(i,j+2);
      phi_ll = 6*phi(i,j) -8*phi(i,j+1) + 3*phi(i,j+2);
      phyy_l = (phi(i,j) - 2*phi_l + phi_ll )/dydy;
    end

    if j < n + 1
      if j==n
	phi_r = 3*phi(i,j+1) - 3*phi(i,j) + phi(i,j-1);
        phyy_r = (phi_r - 2*phi(i,j+1) + phi(i,j) )/dydy;
      else
        phyy_r = (phi(i,j+2) - 2*phi(i,j+1) + phi(i,j) )/dydy;
      end
    else
      phi_r = 3*phi(i,j) - 3*phi(i,j-1) + phi(i,j-2);
      phi_rr = 6*phi(i,j) -8*phi(i,j-1) + 3*phi(i,j-2);
      phyy_r = (phi_rr - 2*phi_r + phi(i,j) )/dydy;
    end

    if j==1
      phi_l = 3*phi(i,j) - 3*phi(i,j+1) + phi(i,j+2);
      phyy_o = (phi(i,j+1) - 2*phi(i,j) + phi_l )/dydy;
      elseif j==n+1
        phi_r = 3*phi(i,j) - 3*phi(i,j-1) + phi(i,j-2);
        phyy_o = (phi_r - 2*phi(i,j) + phi(i,j-1) )/dydy;;
      else
	phyy_o = (phi(i,j+1) - 2*phi(i,j) + phi(i,j-1) )/dydy;
    end

    grad_l = phy_l + dy*0.5*absmin(phyy_l, phyy_o);
    grad_r = phy_r - dy*0.5*absmin(phyy_r, phyy_o);