PERBANDINGAN METODE ADAPTIVE SIMPSON DAN METODE COMPOSITE BOOLE DALAM PENYELESAIAN INTEGRAL NUMERIK BERBASIS PHP

Abstract

The calculation of integrals for nonlinear functions is often difficult to solve analytically, making numerical integration methods necessary to produce approximate results with high accuracy and computational efficiency. This study aims to compare the performance of the Adaptive Simpson and Composite Boole methods in numerical integration through a PHP-based implementation. The research employed a true experimental method by applying both methods to polynomial, exponential, and trigonometric test functions with known exact integral values as benchmarks. The performance of the two methods was evaluated based on absolute error, relative error, and program execution time. The results indicate that both methods produce integral values that are very close to the exact values. The Adaptive Simpson method achieved an average error of 0.07495, which is lower than that of the Composite Boole method 0.07513, indicating higher accuracy. In contrast, the Composite Boole method recorded an average execution time of 0.00059 ms, which is faster than the Adaptive Simpson method with an average execution time of 0.20053 ms. Therefore, the Adaptive Simpson method is more suitable for functions with sharp variations, whereas the Composite Boole method is more effective for relatively smooth functions. Accordingly, the selection of a numerical integration method should be adjusted to the characteristics of the function being integrated as well as the required level of accuracy and computational efficiency.