Integral Approximation Project

Overview

This project focuses on the numerical approximation of integrals using Chebyshev polynomials. It implements and compares the Trapezoidal and Simpson's methods for integral approximation.

Features

• Implements numerical integration using Trapezoidal and Simpson's methods.
• Utilizes Chebyshev polynomials of the first and second kind.
• Includes error measurement and optimization techniques.

Usage

1. Add the project folders to the MATLAB search path.
2. Use provided functions (trapezoidal, simpson, chebyshev_combination) for integral calculations.
3. Explore the GUI application (examplesGUI.mlapp) for visual demonstration and error analysis.

Examples

• Several examples (chebyshev_example_1, chebyshev_example_2, etc.) are provided to demonstrate the effectiveness of the methods in different scenarios.

Error Analysis

• The project includes a detailed analysis of the errors associated with each method, including heat maps and relative error comparisons.

Authors

• Hubert Kowalski
• Adam Kaniasty

Date

• 25.11.2023