Numerical Methods in Python

Numerical methods implementation in Python.

For the implementation in MATLAB, see this repository.

Getting Started

Prerequisites

Using Conda (recommended)

conda env create
conda activate numerical-methods

Using Pip

pip install -r requirements.txt

Using Ubuntu

This section assumes Ubuntu 18.04 (also tested on Ubuntu 22.04), but the procedure is similar for other Linux distributions.

sudo apt -y install python3-numpy

Running the examples

To run the main example, use:

python3 main.py

Implementations

Limits

• Epsilon-delta method

Solutions of equations

• Bisection method
• Secant method
• Regula Falsi method (False Position)
• Pegasus method
• Muller method
• Newton method

Interpolation

• Lagrange method
• Newton method
• Gregory-Newton method
• Neville method

Algorithms for polynomials

• Briot-Ruffini method
• Newton's Divided-Difference method
• Limits of the real roots

Numerical differentiation

• Backward-difference method
• Three-Point method
• Five-Point method

Numerical integration

• Composite Trapezoidal method
• Composite 1/3 Simpson's method
• Romberg method

Initial-value problems for ordinary differential equations

• Euler's method
• Taylor's (Order Two) method
• Taylor's (Order Four) method
• Runge-Kutta (Order Four) method

Systems of differential equations

• Runge-Kutta (Order Four) method

Methods for Linear Systems

• Gaussian Elimination
• Backward Substitution
• Forward Substitution

Iterative Methods for Linear Systems

• Jacobi method
• Gauss-Seidel method