Development of Graphical User Interface (GUI) for Numerical Integration with Application

Abstract

Numerical integration is a key technique for approximating definite integrals, especially when analytical solutions are difficult or impossible to obtain. Although various numerical methods exist, most tools lack an intuitive interface for comparing their efficiency and accuracy. This study develops a MATLAB-based Graphical User Interface that implements five selected integration methods which are Gaussian Quadrature, Simpson’s 1/3 Rule, Simpson’s 3/8 Rule, the Trapezoidal Rule, and the Midpoint Rule. The Graphical User Interface, designed using MATLAB Application Designer, enables users to input functions, define integration limits, step sizes, and subintervals, and provides tables, graphs, and error analyses for result visualization. Comparative evaluations, including case studies and applications in fluid dynamics, option pricing, and medical dosage, demonstrate that Gaussian Quadrature consistently delivers the highest accuracy, followed by Simpson’s 1/3 Rule and Simpson’s 3/8 Rule, while the Midpoint and Trapezoidal Rules yield larger errors. The proposed tool facilitates clear performance comparison and supports informed method selection, making it well-suited as an educational platform that enhances accessibility and understanding of numerical integration methods.