# PERBANDINGAN SOLUSI SISTEM PERSAMAAN NONLINEAR MENGGUNAKAN METODE NEWTON-RAPHSON DAN METODE JACOBIAN

• NANDA NINGTYAS RAMADHANI UTAMI Faculty of Mathematics and Natural Sciences, Udayana University
• I NYOMAN WIDANA Faculty of Mathematics and Natural Sciences, Udayana University
• NI MADE ASIH Faculty of Mathematics and Natural Sciences, Udayana University

### Abstract

System of nonlinear equations is a collection of some nonlinear equations. The Newton-Raphson method and Jacobian method are methods used for solving systems of nonlinear equations. The Newton-Raphson methods uses first and second derivatives and indeed does perform better than the steepest descent method if the initial point is close to the minimizer. Jacobian method is a method of resolving equations through iteration process using simultaneous equations. If the Newton-Raphson methods and Jacobian methods are compared with the exact value, the Jacobian method is the closest to exact value but has more iterations. In this study the Newton-Raphson method gets the results faster than the Jacobian method (Newton-Raphson iteration method is 5 and 58 in the Jacobian iteration method). In this case, the Jacobian method gets results closer to the exact value.

### Author Biographies

NANDA NINGTYAS RAMADHANI UTAMI, Faculty of Mathematics and Natural Sciences, Udayana University
Jurusan Matematika, FMIPA Universitas Udayana
I NYOMAN WIDANA, Faculty of Mathematics and Natural Sciences, Udayana University
Jurusan Matematika, FMIPA Universitas Udayana
NI MADE ASIH, Faculty of Mathematics and Natural Sciences, Udayana University
Jurusan Matematika, FMIPA Universitas Udayana
Published
2013-05-31
How to Cite
RAMADHANI UTAMI, NANDA NINGTYAS; WIDANA, I NYOMAN; ASIH, NI MADE. PERBANDINGAN SOLUSI SISTEM PERSAMAAN NONLINEAR MENGGUNAKAN METODE NEWTON-RAPHSON DAN METODE JACOBIAN. E-Jurnal Matematika, [S.l.], v. 2, n. 2, p. 11-17, may 2013. ISSN 2303-1751. Available at: <https://ojs.unud.ac.id/index.php/mtk/article/view/6286>. Date accessed: 09 june 2023. doi: https://doi.org/10.24843/MTK.2013.v02.i02.p032.
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### Keywords

System of nonlinear equations; Newton-Raphsonâ€™s method; Jacobianâ€™s method