A fourth-order exponential time differencing (ETD) Runge-Kutta scheme with dimensional splitting is developed to solve multidimensional non-linear systems of reaction-diffusion equations (RDE). By approximating the matrix exponential in the scheme with the A-acceptable Pad\'e (2,2) rational function, the resulting scheme (ETDRK4P22-IF) is verified empirically to be fourth-order accurate for several RDE. The scheme is shown to be more efficient than competing fourth-order ETD and IMEX schemes, achieving up to 20 times speed in CPU time. Inclusion of up to three pre-smoothing steps of a lower order L-stable scheme facilitates efficient damping of spurious oscillations arising from problems with non-smooth initial/boundary conditions.

翻译：针对多维非线性反应扩散方程系统，本文发展了一种结合维度分裂的四阶指数时间差分龙格-库塔格式。通过采用A-可接受的Padé(2,2)有理函数逼近格式中的矩阵指数项，所提出的格式（ETDRK4P22-IF）经多个反应扩散方程的数值验证，其精度稳定达到四阶。与同类四阶ETD格式及IMEX格式相比，该格式展现出更优的计算效率，CPU耗时最高可降低20倍。引入低阶L-稳定格式的三步预光滑处理，可有效抑制因非光滑初边值问题引发的虚假振荡现象。