https://github.com/valinsogna/finitediffpdesolver

An insightful collection of finite difference methods to solve elliptic PDEs. This repository provides interactive exercises, from basic grid generation to advanced boundary value problem solutions, using forward Euler methods. Dive in to explore and understand the dynamics of PDEs through hands-on tasks.
https://github.com/valinsogna/finitediffpdesolver

finite-difference-method numerical-analysis pde-solver

Last synced: 11 months ago
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An insightful collection of finite difference methods to solve elliptic PDEs. This repository provides interactive exercises, from basic grid generation to advanced boundary value problem solutions, using forward Euler methods. Dive in to explore and understand the dynamics of PDEs through hands-on tasks.

• Host: GitHub
• URL: https://github.com/valinsogna/finitediffpdesolver
• Owner: valinsogna
• License: mit
• Created: 2023-09-19T09:21:43.000Z (over 2 years ago)
• Default Branch: main
• Last Pushed: 2023-09-19T09:23:25.000Z (over 2 years ago)
• Last Synced: 2025-01-22T15:36:40.540Z (about 1 year ago)
• Topics: finite-difference-method, numerical-analysis, pde-solver
• Language: Jupyter Notebook
• Homepage:
• Size: 104 KB
• Stars: 0
• Watchers: 1
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# Finite Difference Methods for PDEs

This repository contains implementations and solutions for exercises related to the finite difference methods to solve Partial Differential Equations (PDEs).

## Contents

- **Exercise One:** Implementation of a finite difference method to approximate the solution of an elliptic PDE.

- **Exercise Two:** Studying the convergence of the method from the first exercise.

- **Exercise Three:** Analyzing the behavior of the solution from exercise one when the domain is changed.

- **Exercise Four:** Investigating the effect of the source term on the solution's behavior.

- **Exercise Five:** Time-dependent variation of the original PDE problem and solving it using the forward Euler's method.

- **Exercise Six:** Implementation of an algorithm to compute the eigenvalues and eigenvectors of a matrix using LU factorization.

## Highlights

- **Spatial Discretization:** The project showcases different approaches to discretize the spatial component of the PDE.

- **Time-dependent Variation:** Exercise Five introduces time-dependence and demonstrates how to handle it with a forward Euler's approach.

- **Eigenvalues and Eigenvectors:** The sixth exercise dives deep into the computation of the eigenvalues and eigenvectors for a matrix using LU factorization.

## Dependencies

- Python 3

- Matplotlib

- NumPy

## Contribute

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

## License

[MIT](https://choosealicense.com/licenses/mit/)

Remember to modify the GitHub link to point to your actual repository link. Also, adjust the Usage section based on your project structure, and update any image links accordingly.