Advection-Diffusion Equations

This lecture covers the numerical solution of advection-diffusion equations, stability analysis using Von Neumann method, and properties of analytical solutions. It discusses the explicit finite difference scheme, stability conditions, and the behavior of solutions over time. The instructor demonstrates the properties of the solutions and tests them numerically. The lecture also explores the stability of different numerical schemes and the impact of diffusion on the solutions. Additionally, it delves into the analytical properties of the solutions and their behavior under various initial conditions.