García-Archilla et al. integrate POD-ROM for semilinear reaction-diffusion with BDF-q (q≤5) time stepping, proving and numerically confirming optimal order-q temporal convergence
For a semilinear reaction-diffusion model problem, the authors combine a POD reduced-order model built on first-order difference-quotient snapshots with BDF-q (1≤q≤5) time integration, prove optimal order-q convergence in time via G-stability analysis, and observe numerical convergence slopes consistent with the theory on the diffusive Brusselator system.