Reaction-diffusion-advection equations provide precise interpretations for many important phenomena in complex interactions between natural and artificial systems. This paper studies second-order semi-discretizations for the numerical solution of reaction-diffusion-advection equations modeling quenching types of singularities occurring in numerous applications. Our investigations particularly focus at cases where nonuniform spatial grids are utilized. Detailed derivations and analysis are accomplished. Easy-to-use and highly effective second-order schemes are acquired. Computational experiments are presented to illustrate our results as well as to demonstrate the viability and capability of the new methods for solving singular quenching problems on arbitrary grid platforms.

中文翻译：

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求解任意空间网格上的随机淬火模型的二阶半离散方案

反应扩散对流方程为自然系统和人工系统之间复杂相互作用中的许多重要现象提供了精确的解释。本文研究了反应扩散对流方程的数值解的二阶半离散化，该方程对许多应用中出现的奇异点的猝灭类型进行了建模。我们的研究特别关注使用非均匀空间网格的情况。详细的推导和分析已完成。获得了易于使用和高效的二阶方案。提出了计算实验，以说明我们的结果，并证明了在任意网格平台上解决奇异淬火问题的新方法的可行性和能力。