I would like to reproduce the workflow laid out by Hacker & Uecker (2009). The project has three key steps: 1. Discretise my time-dependent PDE in space so it becomes a large, stiff ODE system. 2. Advance that system with an implicit time-integration routine. 3. Use Newton iterations at every step to guarantee stable solutions over long time horizons. I will supply the exact PDE and boundary conditions once we start. Finite-difference, finite-volume, or spectral discretisations are all acceptable as long as the stability matches the paper’s results. The final deliverable should include: • Well-commented source code (Python, MATLAB, or a language you propose) • A short write-up or notebook showing that the implementation reproduces the stable time-dependent behaviour highlighted in the reference paper • Clear instructions so I can rerun the simulations on my own machine If you have experience with stiff ODE solvers, implicit schemes, and Newton iterations, I’d love to hear how you would approach this.