Numerical Methods Extension for stdlib

This project extends the @stdlib library with additional numerical methods for differentiation and integration, along with visual demonstrations of their performance.

Project Overview

This repository demonstrates both existing stdlib functions and new numerical methods implementations for:

• Numerical differentiation (forward and backward difference methods)
• Numerical integration (trapezoidal rule and Simpson's rule)
• Analysis and comparison of these methods with exact solutions

Repository Structure

• already.js - Demonstrates existing stdlib functions and capabilities
• index2.js - Contains implementations of numerical methods not directly available in the stdlib library
• index.html - Web visualization interface for demonstrating the performance of the numerical methods

Setup Instructions

Prerequisites

• Node.js and npm installed
• Git installed

Steps to Run the Project

1. Clone the repository

git clone https://github.com/your-username/stdlib-numerical-methods.git

cd stdlib-numerical-methods

2. Install dependencies

npm install

3. Run the demonstrations

To see existing stdlib functions in action node already.js

To run the numerical methods showcase node index2.js

4. View the visualization

Option 1: Open index.html directly in a browser

Option 2: Use a local server

Option 3: Use VS Code's Live Server extension

Features Demonstrated

Existing stdlib Functions (already.js)

• Special mathematical functions (gamma, beta, Bessel, error function)
• Array operations
• Basic statistics
• Simple integration and differentiation approximations

New Numerical Methods (index2.js)

Differentiation Methods

• Forward difference method
• Backward difference method

Integration Methods

• Trapezoidal rule
• Simpson's rule

Analysis Tools

• Error comparison with exact solutions
• Convergence testing
• Performance visualization

Web Visualization (index.html)

• Interactive comparison of numerical methods
• Error analysis charts
• Convergence visualization
• Performance metrics tables

Contributing

• Fork the repository
• Create a feature branch (git checkout -b feature/amazing-feature)
• Commit your changes (git commit -m 'Add some amazing feature')
• Push to the branch (git push origin feature/amazing-feature)
• Open a Pull Request

Acknowledgments

• Based on the @stdlib project
• Inspired by classical numerical analysis techniques