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：我们提出了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。该格式基于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，实现了简单而高效的实现。该过程可自然推广至任意数量的组分和任意空间维度。针对物理相关的（对流型）Schnakenberg、FitzHugh-Nagumo、DIB及对流型Brusselator模型进行的多个二维和三维数值算例，清晰展示了该方法相较于当前先进技术的优势。