HeatWave: Numerical Solutions and Analysis of the Heat Equation

• Tech Stack: Python, NumPy, Matplotlib
• Github URL: Project Link

During our mathematics classes, I collaborated with two other students to solve the heat equation in both one and two dimensions. This project includes two Python codes, several video examples, and a PDF document that explains the theoretical background and analysis of the numerical approach.

The PDF offers a theoretical exploration of the heat equation, analyzing the numerical schema with respect to its consistency, stability (Von Neumann-Fourier stability), and convergence. The Python files consist of "Resolution_equation_heat" which defines a class `EqHeat` with a constructor and methods, and "Resolution_equation_heat_main," which is editable for modifying the initial conditions. Examples of different initial conditions are provided for experimentation.

Additionally, video demonstrations of the heat equation in two dimensions under various initial conditions are included to visually represent the results.