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

• 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.

• 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.

• Python 3
• Matplotlib
• NumPy

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

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.