Perbandingan Metode Newton Raphson dan Metode Steffensen dalam Penentuan Akar Fungsi Non-Linier Menggunakan Pemrograman Hypertext Preprocessor

Abstract

Mathematical problems frequently arise in various scientific fields, particularly in determining the roots of nonlinear functions. Since complex nonlinear functions are often difficult to solve analytically, numerical methods are commonly used as an alternative approach. This article aims to compare the number of iterations and the error levels produced by the Newton-Raphson and Steffensen methods. The tests were conducted on three types of functions, polynomial functions of the form a1xn+a2xn-1+...+amx0, exponential functions of the form aebx+d+t and trigonometric functions of the form a0sin(b0x)+a1cos(b1x)+a2. For each type, three different functions were used, and each was tested with three different initial guesses. The results show that, in terms of iteration count, the Newton-Raphson method outperformed the Steffensen method for polynomial and trigonometric functions by 84% and 62%, respectively, while for exponential functions, the Steffensen method was superior by 12%. In terms of error, the Newton-Raphson method yielded smaller errors across all function types, with improvements of 92%, 84%, and 98% for polynomial, exponential, and trigonometric functions, respectively, compared to the Steffensen method.