Turing-region preservation in matrix-oriented splitting methods for reaction-diffusion systems (opens in new tab)

We develop matrix-oriented formulations of first-order splitting integrators for two-species reaction-diffusion systems on 2D domains, using the Gierer-Meinhardt system as a benchmark for discrete Turing instability. Exploiting the differential matrix equation associated with tensor-product spatial discretizations, we obtain the families IE-S and EX-S, where the diffusive flow is treated by implicit Euler or exactly, respectively, and the reacti...