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Numerical Analysis Methods

Welcome to the Numerical Analysis Methods repository! This project is designed to implement and demonstrate various numerical methods for solving mathematical problems, such as finding roots, solving differential equations, and performing numerical integration.

This repository is ideal for students and professionals looking to understand and apply numerical techniques in programming. All methods are implemented with well-documented code, including explanations and examples.

🔢 Methods Implemented

Here’s a list of the numerical methods you will find in this repository:

1. Root-Finding Algorithms

  • Bisection Method

    • A simple bracketing method that finds the root by successively halving the interval.

  • Newton-Raphson Method

    • A powerful root-finding algorithm that uses derivatives to quickly converge to a solution.

  • False Position Method (Regula Falsi)

    • Similar to the bisection method but with better convergence properties.

  • Secant Method

    • An iterative method that does not require derivatives and improves upon the false position method.

2. Numerical Integration

  • Trapezoidal Rule

    • A technique to approximate definite integrals by dividing the area under the curve into trapezoids.

  • Simpson's Rule

    • An advanced technique that uses parabolic segments for better accuracy in approximating integrals.

3. Linear Algebraic Solvers

  • Gauss-Seidel Method

    • An iterative method to solve systems of linear equations.

  • Jacobi Iteration Method

    • Another iterative method, similar to Gauss-Seidel, for solving linear systems.

4. Differential Equations Solvers

  • Euler's Method

    • A simple, first-order method for solving ordinary differential equations (ODEs).

  • Runge-Kutta Methods

    • More advanced methods for solving ODEs with higher accuracy, including the popular RK4 method.

📂 Structure of the Repository

Each method is stored in a separate files and includes:

  • The code implementation in C++ Python (or other programming languages).
  • Algorithm for each Method is in Algorithms.md file.
  • You can view the detailed algorithms here.

💻 How to Use

  1. Clone this repository to your local machine: 
    git clone https://github.com/wasiif/NumericalAnalysis.git

🌟 Contributions

Contributions are highly welcome! Feel free to fork this repository and submit pull requests for:

  • New numerical methods.
  • Optimizations or improvements to existing methods.
  • Bug fixes or additional language implementations (Python, Java, etc.).