/numerical-methods-python

Numerical methods implementation in Python.

Primary LanguagePythonMIT LicenseMIT

Numerical Methods in Python Actions Status

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