  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.
