We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary 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. Several numerical examples in 2D and 3D with physically relevant (advective) Schnakenberg, FitzHugh--Nagumo, DIB, and advective Brusselator models clearly show the advantage of the approach against state-of-the-art techniques.

翻译：我们提出一种适用于二维和三维空间中双组分耦合刚性演化对流-扩散-反应方程组的二阶指数格式。该方法基于矩阵函数的方向分裂，通过计算小规模指数型函数与张量-矩阵乘积实现简单高效的数值实现。该过程可直接推广至任意数量的组分及空间维度。二维与三维空间中若干具有物理意义的（对流型）Schnakenberg模型、FitzHugh-Nagumo模型、DIB模型以及对流型Brusselator模型的数值算例表明，该方法相较于现有前沿技术具有明显优势。