Monte Carlo and Gauss-Legendre Integration Methods

This repository contains implementations of two numerical integration techniques using MATLAB: Monte Carlo Integration and Gauss-Legendre Quadrature.

Table of Contents

• Introduction
• Methods
  • Monte Carlo Integration
  • Gauss-Legendre Quadrature
• Content

Introduction

Numerical integration is a fundamental technique in applied mathematics and computational sciences. While exact analytical solutions to integrals may not always exist, numerical approaches can provide accurate approximations. This repository demonstrates two popular approaches:

1. Monte Carlo Integration: A probabilistic method relying on random sampling.
2. Gauss-Legendre Quadrature: A deterministic method using optimized sampling points (roots of Legendre polynomials).

Methods

Monte Carlo Integration

Monte Carlo Integration estimates the value of an integral by using random samples. It is particularly useful for higher-dimensional integrals or when the integration domain is irregular.

Gauss-Legendre Quadrature

Gauss-Legendre Quadrature is a more precise method, especially for integrals over fixed domains. It uses specific sample points and weights derived from the roots of Legendre polynomials to approximate the integral.

Content

• Report/writeup.pdf: Summarizes the results of the numerical integration methods.
• src/Monte_Carlo_and_Gauss_Legendre_Integration.mlx: Contains the MATLAB code implementing the Monte Carlo and Gauss-Legendre integration techniques.