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Numerical Integration in C++

This project implements and compares several numerical integration methods in C++.
It was created as a small playground to practice and improve my C++ programming skills while working with classical numerical algorithms.

Implemented Methods

  • Trapezoidal Rule
  • Simpson’s Rule
  • Monte Carlo Integration

Each numerical result is compared to an analytical solution to compute absolute errors.

Features

  • Arbitrary functions via function pointers
  • Analytical reference integrals for validation
  • Runtime measurement using std::chrono
  • Error analysis for increasing numbers of intervals
  • Export of error data to CSV

Error Analysis & Visualization

  • Error data is written to data/errors.csv and not published on github
  • A Jupyter notebook is included that loads this file and visualizes the convergence behavior of the different methods

Project Structure

. 
├── src/
│ └── main.cpp
│ └── integration.h
│ └── integration.cpp
├── data/
│ └── errors.csv
├── plots/
│ └── making_plots.ipynb
└── Makefile

Purpose

This project was used to experiment with:

  • Numerical integration techniques
  • Clean C++ code structure
  • Basic performance and error analysis