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.
Highlights
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 does perform better than the steepest descent method if the initial point is close to the minimizer
Summary
Sistem persamaan nonlinear merupakan kumpulan dari beberapa persamaan nonlinear dengan fungsi tujuannya saja atau bersama dengan fungsi kendala berbentuk nonlinier, yaitu pangkat dari variabelnya lebih dari satu [6]. Ada beberapa fungsi tujuan dalam persamaan nonlinier yang tidak bisa diselesaikan secara analitik, tetapi dapat diselesaikan dengan metode-metode khusus untuk penyelesaian masalah dalam persamaan nonlinier. Ada banyak macam metode numerik untuk menyelesaikan sistem persamaan linear maupun sistem persamaan nonlinear diantaranya metode Newton-Raphson dan metode Jacobian. Metode Newton-Raphson adalah metode untuk mencari hampiran atau pendekatan terhadap akar fungsi real [1]. Secara umum pembahasan metode Newton-Raphson yang digunakan menggunakan pendekatan polinomial Taylor: Pn x = f x0 + f′ x0 x − x0. Dimana penyelesaiannya dengan perluasan metode Newton-Raphson melalui ekspansi deret taylor pada masing-masing persamaan. Metode Jacobian adalah metode penyelesaian persamaan melalui proses iterasi dengan menggunakan persamaan [2]: xi(k+1) = bi−. N maka sistem persamaan iterasinya dapat ditulis sebagai berikut : x1(k+1) =. Tebakan yang terlalu jauh dari solusi sejatinya dapat menyebabkan iterasi divergen
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