  A second-order $L$-stable exponential time-differencing (ETD) method is
developed by combining an ETD scheme with approximating the matrix exponentials
by rational functions having real distinct poles (RDP), together with a
dimensional splitting integrating factor technique. A variety of non-linear
reaction-diffusion equations in two and three dimensions with either Dirichlet,
Neumann, or periodic boundary conditions are solved with this scheme and shown
to outperform a variety of other second-order implicit-explicit schemes. An
additional performance boost is gained through further use of basic
parallelization techniques.
