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All Projects → cfgnunes → numerical-methods-python

cfgnunes / numerical-methods-python

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Numerical methods implementation in Python.

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python
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newtonlinear-systemsdifferential-equationsnumerical-methodstaylornumerical-analysisrunge-kutta

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Numerical Methods 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-env

Using Pip

pip install -r requirements.txt

Using Ubuntu

This section assumes Ubuntu 16.04 (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

Solutions of equations

  • Bisection method
  • Newton method
  • Secant method

Interpolation

  • Lagrange method
  • Neville method

Algorithms for polynomials

  • Briot-Ruffini method
  • Newton's Divided-Difference method

Numerical differentiation

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

Numerical integration

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