Comparison of Gauss-Seidel Method, Newton-Raphson Method, and Broyden Method in Solving Nonlinear Equation Systems

Agus Sutrisno; Dorrah Azis; Arvi Hasanah; Tiryono Ruby; Nonik Mega

doi:10.59890/ijasse.v3i1.292

Authors

Agus Sutrisno University of Lampung
Dorrah Azis University of Lampung
Arvi Hasanah University of Lampung
Tiryono Ruby University of Lampung
Nonik Mega University of Lampung

DOI:

https://doi.org/10.59890/ijasse.v3i1.292

Keywords:

Nonlinear Equation Systems, Gauss-Seidel Method, Newton-Raphson Method, Broyden Method

Abstract

A nonlinear equation system is a set of nonlinear equations that tend to be difficult to solve analytically. One common approach used to solve a nonlinear equation system is numerically in the form of an iteration method, which produces solutions in the form of approximate values or approximations. There are many numerical methods that can be applied to solve a nonlinear equation system, such as the Gauss-Seidel Method, the Newton-Raphson Method, and the Broyden Method. To obtain an effective and efficient solution, the selection of the right method is required. Therefore, this study will compare the performance of the Gauss-Seidel Method, the Newton-Raphson Method, and the Broyden Method in solving a nonlinear equation system. This study uses MATLAB software to assist in the process of solving a nonlinear equation system. The results of the study show that the Newton-Raphson Method is more effective in solving a nonlinear equation system compared to the Gauss-Seidel Method and the Broyden Method.

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