  We present two approaches for enhancing the accuracy of second order finite
difference approximations of two-dimensional semilinear parabolic systems.
These are the fourth order compact difference scheme and the fourth order
scheme based on Richardson extrapolation. Our interest is concentrated on a
system of ten parabolic partial differential equations in air pollution
modeling. We analyze numerical experiments to compare the two approaches with
respect to accuracy, computational complexity, non-negativity preserving and
etc. Sixth-order approximation based on the fourth-order compact difference
scheme combined with Richardson extrapolation is also discussed numerically.
