I am investigating gravity-driven liquid films flowing over a corrugated substrate with an extended WIBL model, and the base solution is strictly periodic. The next step is a full Floquet stability analysis of that periodic state so I can identify the short-wave instability noses and the curious stability islands created by the substrate’s geometry. All governing equations and parameter ranges are ready; what I still need is a clean, reproducible Floquet framework that extracts the multipliers for each wavenumber and returns clear stability maps. You are free to work in MATLAB, Python (NumPy/SciPy), or Julia as long as the code is well commented and numerically robust—spectral collocation or a high-order finite-difference approach is fine as long as convergence is demonstrated. Deliverables • A runnable script or notebook that assembles the monodromy matrix for the periodic WIBL coefficients and computes the Floquet multipliers across user-defined parameter grids • Plots that highlight the predicted instability noses and stability islands, ready for publication (vector format preferred) • A concise technical note summarising the formulation, numerical method, verification checks, and how to reproduce the figures Acceptance criteria: the dominant multiplier spectrum must match my reference case within 1 % and the code must complete a typical parametric sweep (200 wavenumbers × 50 Reynolds numbers) in under 10 minutes on a standard laptop. Feel free to suggest efficiency tweaks or alternative numerical schemes if they improve accuracy without sacrificing clarity.