  For elliptic interface problems with discontinuous coefficients, the maximum
accuracy order for compact 9-point finite difference scheme in irregular points
is three [7]. The discontinuous coefficients usually have abrupt jumps across
the interface curve in the porous medium of realistic problems, causing the
pollution effect of numerical methods. So, to obtain a reasonable numerical
solution of the above problem, the higher order scheme and its effective
implementation are necessary. In this paper, we propose an efficient and
flexible way to achieve the implementation of a hybrid (9-point scheme with
sixth order accuracy for interior regular points and 13-point scheme with fifth
order accuracy for interior irregular points) finite difference scheme in
uniform meshes for the elliptic interface problems with discontinuous and
high-contrast piecewise smooth coefficients in a rectangle $\Omega$. We also
derive the $6$-point and $4$-point finite difference schemes in uniform meshes
with sixth order accuracy for the side points and corner points of various
mixed boundary conditions (Dirichlet, Neumann and Robin) of elliptic equations
in a rectangle. Our numerical experiments confirm the flexibility and the sixth
order accuracy in $l_2$ and $l_{\infty}$ norms of the proposed hybrid scheme.
