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Numerical Methods for Physics – Set of projects

This repository contains a series of laboratory projects completed during the Computer physics course. The projects focus on the practical implementation of mathematical algorithms to solve physics-based problems using Python.

🛠 Tech Stack

  • Language: Jupyter Notebook
  • Core Libraries: NumPy, Matplotlib

📂 Project Highlights

1. Ordinary Differential Equations (ODEs) & Modeling

  • Explicit & Implicit Solvers: Implementation of various schemes (Euler, Runge-Kutta, RK2, RK4) to solve autonomous problems and harmonic oscillations (damped and driven).
  • Epidemic Modeling (SIR): Application of implicit methods to simulate the spread of infectious diseases.
  • Stiff Problems: Using adaptive time-stepping to maintain stability in computationally challenging systems.
  • Kuramoto Model (Neurobiology): Simulating large-scale synchronization of oscillators, representing neural network activity or collective biological behavior.

2. Wave Dynamics & Eigenvalues

  • Shooting Method (Project 9): Finding the normal modes (eigenvalues) of a 1D vibrating string.
  • Verlet Method (Project 10): Solving the 1D wave equation using the Verlet algorithm to ensure energy conservation during string vibration simulations.

3. Partial Differential Equations (PDEs)

  • Poisson Equation: Solving static field problems using global and local relaxation techniques.
  • Multigrid Acceleration: Using hierarchical grids to significantly speed up the convergence of PDE solvers.

4. Stochastic Methods

  • Monte Carlo Integration: Using probabilistic sampling to compute high-dimensional integrals where traditional quadrature fails.

📈 Key Concepts Learned

  • Stability & Convergence: Understanding when and why numerical schemes fail.
  • Vectorization: Leveraging NumPy for high-performance calculations in Python.
  • Physics Modeling: Translating physical laws (Newton, Maxwell, Poisson) into code.

Created as part of the Computer Physics course.