A Comparison Study of Two High Accuracy Numerical Methods for a Parabolic System in Air Pollution Modelling

TL;DR

This paper compares two high-accuracy numerical methods, the compact difference scheme and Richardson extrapolation, for solving a system of parabolic PDEs in air pollution modeling, highlighting their accuracy and computational efficiency.

Contribution

It provides a comparative analysis of two advanced numerical schemes and introduces a sixth-order approximation for improved accuracy in air pollution PDE models.

Findings

The fourth order compact difference scheme offers high accuracy with moderate complexity.

Richardson extrapolation enhances the accuracy of second order schemes effectively.

The sixth-order approximation further improves solution precision in the tested models.

Abstract

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.