Assignment

PDEs in 2D: Reaction-Diffusion

Complete a 2D reaction-diffusion simulation and report your findings.

Required

1. Implement the 2D Gierer-Meinhardt PDE with a 5-point stencil.
2. Use \(L_1=20\), \(L_2=50\), \(dx=1\), \(dt=0.001\), \(a=0.40\), \(b=1.00\), \(d=20\), \(\gamma=1\).
3. Plot a snapshot of \(v(x,y)\) after a long integration.
4. Create an animation that updates \(v(x,y)\) in real time.

Turing Instability

5. Implement find_unstable_spatial_modes() and report the leading mode for \(d=20\) and \(d=30\).
6. State whether each case exhibits Turing instability.

Gray-Scott (Optional)

• Implement the Gray-Scott model and reproduce one of the parameter sets (A-E).
• Add interaction: draw perturbations and pause/resume the simulation.

Tips for Success

• Start small: use a smaller grid to debug the update function.
• Check dt: if the simulation explodes, reduce \(dt\) or increase \(dx\).
• Validate: compare your pattern to ?@fig-gm-2d in the module notes.

Good luck and enjoy your coding!