Numerical Methods Library

Introduction

This Python library provides a collection of numerical methods for interpolation, root finding, numerical integration, and solving systems of linear equations. It's designed to assist in educational and research activities related to numerical analysis and scientific computing.

Features

• Interpolation Methods: Lagrange interpolation, Piecewise interpolation, and Newton's divided differences.
• Root Finding Methods: Fixed-point iteration, Newton-Raphson method, Secant method, and Steffensen's method.
• Numerical Integration Methods: Simpson's rule, Trapezoidal rule, and Romberg integration.
• Iterative Linear Systems: Methods like Jacobi for solving linear systems iteratively.
• Numerical Derivation Methods: Various derivative approximation techniques.

Dependencies

• Python 3.x
• NumPy
• PrettyTable
• Math

Installation

Clone this repository or download the files directly:

git clone https://github.com/Zero5896/Numerical_methods.git
cd numerical-methods-library

Install the required Python packages:

pip install -r requirements.txt

Usage

To use the library, import the necessary classes from the modules and create instances as needed. Below are some examples of how to use different methods in this library:

Example: Using Root Finding Methods

import numerical_methods.RootFindingMethods

f = lambda x: x**2 - 4
fp = lambda x: 2*x
initial_guess = 2
tolerance = 1e-6
root = numerical_methods.RootFindingMethods.Newton_R(f, fp, initial_guess, TOL=tolerance)
print("Root found:", root)

Example: Using Numerical Integration Methods

import numerical_method.NumericalIntegrationMethods

f = lambda x: x**2
a = 0
b = 1

approximation = numerical_method.NumericalIntegrationMethods.simpsons_rule_N(f, a, b)
print("Approximated integral:", approximation)

Contibuting

Contributions are welcome! If you'd like to contribute, please fork the repository and use a pull request to add your contributions. If you have any suggestions or issues, please open an issue in the repository.