Numerical Methods for Wave Simulations in Python

Understanding how physical waves behave is essential in science and engineering, but solving the underlying equations requires more than just pen and paper. This course bridges the gap between mathematical theory and computational execution, teaching you how to translate complex partial differential equations into functional Python code. You will gain the skills to simulate wave propagation by learning how to discretize space and time using industry-standard techniques. By the end of this program, you will be able to build and evaluate different numerical solvers, understanding the trade-offs between speed and accuracy in scientific computing. What you'll learn: - Understand the fundamental concepts of numerical analysis and wave physics - Implement the finite-difference method to solve one-dimensional wave equations - Apply pseudospectral and spectral element methods for high-accuracy simulations - Practice writing clean Python code using modern type hints and NumPy for mathematical operations - Analyze the stability and convergence of different numerical schemes - Develop computational algorithms to model 2D scalar wave propagation The content begins with essential terminology and the physics of waves, progressing through step-by-step mathematical derivations to the implementation of various numerical solvers. You will work through written explanations and code examples designed to solidify your understanding of how simulations work under the hood. This course is designed for beginners in computational science, physics, or engineering. No prior experience with numerical methods is required, though a basic familiarity with Python syntax is helpful. Start building your own wave simulations through practical numerical modeling.