This repository contains a Python script for solving the Poisson's equation numerically.
The Poisson's equation is an elliptic partial differential equation of the form:
In this framework, we solve the Poisson equation in a 2D domain using the finite difference method. Rewriting the Poisson's equation yields:
where the partial derivatives are computed using the second-order finite differnece method:
Rearanging the above equation yields:
To use this script, you need to have Python installed on your machine. You can download Python here.
You also need to have the following Python libraries installed:
- NumPy
- Matplotlib
You can install these libraries using the following commands:
pip install numpy pip install matlotlib
To run the script, navigate to the directory containing the script and run the following command:
python3 main.py
This will solve the Poisson equation and display the results in a 3D plot.