We propose a second order exponential scheme suitable for two-component coupled systems of stiff advection--diffusion--reaction equations in two and three space dimensions. It is based on a directional splitting of the involved matrix functions, which allows for a simple yet efficient implementation through the computation of small-sized exponential-like functions and tensor-matrix products. The procedure straightforwardly extends to the case of an arbitrary number of components and to any space dimension $d$. Several numerical experiments in 2D and 3D with physically relevant DIB, Schnakenberg, FitzHugh--Nagumo, and advective Brusselator models clearly show the advantage of the approach against state-of-the-art techniques.

翻译：我们提出了一种适用于二维和三维空间中双组分刚性对流-扩散-反应方程组耦合系统的二阶指数格式。该方法基于所涉及矩阵函数的方向分裂，通过计算小规模指数型函数和张量矩阵乘积，能够简单高效地实现。该过程可直接推广至任意数量组分及任意空间维度$d$。在二维和三维空间中，针对物理相关的DIB、Schnakenberg、FitzHugh-Nagumo及对流型Brusselator模型进行的多项数值实验清晰表明，该方法相较于现有先进技术具有明显优势。