Diffusion Equation Solutions in MATLAB with Code Implementation Examples

This presentation includes two detailed examples demonstrating how to solve diffusion equations using MATLAB. The first example focuses on solving one-dimensional diffusion equations, while the second covers two-dimensional diffusion equations. Throughout the computational process, we generate animated visualizations for both 1D and 2D diffusion processes to intuitively demonstrate the calculation progress. The implementations utilize finite difference methods with appropriate stability conditions (like the CFL condition for explicit schemes). Key MATLAB functions employed include pdepe for 1D cases or custom finite difference implementations using matrix operations for efficient computation. For 2D cases, we demonstrate how to handle spatial discretization using meshgrid and surface plotting functions for visualization. Additionally, we explore fundamental concepts and practical applications of diffusion equations, providing readers with deeper insights into the underlying principles and real-world implementation value. The code includes comments explaining boundary condition handling, time-stepping algorithms, and numerical stability considerations essential for accurate simulations.