一种用于空气污染建模的抛物系统中两种高精度数值方法的比较研究
A Comparison Study of Two High Accuracy Numerical Methods for a Parabolic System in Air Pollution Modelling
AI总结：
本文比较了两种高精度数值方法在空气污染建模抛物系统中的应用，分析了精度、计算复杂度和非负性保持等性能。
摘要：
我们提出了两种方法以提高二维半线性抛物系统的二阶有限差分近似精度：四阶紧凑差分方案和基于Richardson外推的四阶方案。我们的关注点是空气污染建模中包含十个抛物偏微分方程的系统。我们通过数值实验比较这两种方法在精度、计算复杂度、非负性保持等方面的性能。还讨论了基于四阶紧凑差分方案和Richardson外推的六阶近似。
英文摘要：
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.
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