A Comparison Study of Two High Accuracy Numerical Methods for a Parabolic System in Air Pollution Modelling
This work provides a comparative analysis of high-accuracy numerical methods for a specific domain (air pollution modeling), but the results are incremental and domain-specific.
The study compares fourth-order compact difference and Richardson extrapolation schemes for solving a system of ten parabolic PDEs in air pollution modeling, finding that both enhance accuracy over second-order methods, with sixth-order accuracy achievable by combining both approaches.
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.