Numerical Methods in Python

Some mathematical problems are difficult to solve directly, and in some cases, finding an exact solution isn't possible. I started this repository out of curiosity to understand how computers can help solve these kinds of problems.

Here, I'm implementing different numerical methods in Jupyter Notebooks using Python and its scientific computing libraries. Along the way, I'm exploring how each method works, how it approaches an approximate solution step by step, and how accuracy and numerical errors affect the results.

Project Structure

numerical-methods-python/
├── root-finding-method/
├── interpolation/
├── numerical-integration/
├── linear-systems/
├── eigenvalues-eigenvectors/
└── differential-equations/

Directory	What's Inside
root-finding-method	• Bisection Method • Newton-Raphson Method • Fixed Point Iteration Method • False Position (Regula Falsi) Method
interpolation	• Newton's Forward Difference • Newton's Backward Difference • Newton's Divided Difference • Lagrange Interpolation • Cubic Spline Interpolation
numerical-integration	• Trapezoidal Rule • Simpson's 1/3 Rule • Simpson's 3/8 Rule • Romberg Method • Gauss-Legendre Quadrature (2-point) • Gauss-Legendre Quadrature (3-point)
linear-systems	• Gauss Elimination • Gauss-Jordan Elimination • Matrix Inversion • LU Decomposition • Jacobi Method • Gauss-Seidel Method
eigenvalues-eigenvectors	• Power Method • Jacobi Method • Givens Method
differential-equations	• Euler's Method • Runge-Kutta 2nd Order (RK2) • Runge-Kutta 4th Order (RK4) • Adams-Bashforth-Moulton Method

Libraries Used

I'm mainly using these Python libraries:

• NumPy for numerical calculations and matrix operations
• SciPy to compare my results with built-in numerical methods
• SymPy for symbolic calculations and derivatives
• Pandas to display iteration steps and results in tables
• Matplotlib to plot graphs and visualize results
• Jupyter Notebook to run the code and see the output step by step

Getting Started

You'll need Python 3 and pip installed on your computer.

First, install the required libraries:

python -m pip install numpy scipy sympy pandas matplotlib notebook

Clone the repository:

git clone https://github.com/donish0/numerical-methods-python.git
cd numerical-methods-python

Start Jupyter Notebook from the project folder:

jupyter notebook

If the jupyter command is not found, use this instead:

python -m notebook

Your browser will open the Jupyter file explorer. Go to the folder containing the method you want to try and open the .ipynb notebook.

For example, open root-finding-method/bisection.ipynb and run the cells one by one (Shift + Enter), or use Run All from the menu.

You can also open the notebooks in VS Code (with the Jupyter extension installed) or in Google Colab (open them from the GitHub tab or upload the file).

You can explore the other folders in the same way.

What I'm Learning

• How different numerical methods work and the math behind them
• Implementing the algorithms myself instead of just relying on built-in functions
• How iterative methods get closer to a solution step by step
• How accuracy, convergence, and numerical errors affect the results
• Visualizing results with graphs to understand how each method behaves
• Improving my Python and problem-solving skills with each method

License

This project is open source under the MIT License.