Numerical Methods

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Numerical methods implementation in Python 3.

For the "MATLAB version", see this repository.

Getting Started

Prerequisites

This section assumes Ubuntu 16.04 (also tested on Ubuntu 18.04), but the procedure is similar for other Linux distributions. The prerequisites is to install the following packages:

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

Built With

• Python - Programming language used

Authors

• Cristiano Nunes - Developer