Perbandingan Metode Steffensen dan Metode Brent dalam Penyelesaian Masalah Break Even Point Menggunakan PHP

Abstract

The nonlinear mathematical model of the Break Even Point (BEP) problem is difficult to solve analytically to obtain an exact solution; therefore, numerical methods can serve as an alternative approach to address this issue. Based on this, the present study aims to develop a PHP program for solving the BEP problem and to compare Steffensen’s and Brent’s methods in terms of error and number of iterations. This research used the experimental method, whose implementation procedures include preparation, PHP program development, program testing, program revision, analysis, and conclusion. The PHP-based program developed in this study can serve as an alternative tool for solving BEP problems and is accessible to both practitioners and academics via the following link: https://lpptp.fkip.unram.ac.id/smhs/e1r021001/index.php. In solving the BEP problem, the error of Steffensen’s method was 17,3 x 10^-8, while the error of Brent’s method was 6,4 x 10^-8, therefore the error produced by the Brent’s method is smaller than that of the Steffensen’s method because 6,4 x 10^-8 < 17,3 x 10^-8. Additionally, the number of iterations required by Steffensen’s method was 109, whereas the number of iterations of Brent’s method was 56, therefore, the number of iterations of Brent’s method is fewer than that of Steffensen’s method because 56 < 109. Consequently, it can be concluded that Brent’s method is more effective than Steffensen’s method in solving BEP problems in terms of both error and number of iterations.