Abstract
We present two approaches for enhancing the accuracy of the 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, nonnegativity preserving, etc. The sixth-order approximation based on the fourth-order compact difference scheme combined with Richardson extrapolation is also discussed numerically.
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