SOLUSI NUMERIK PERSAMAAN NON-LINIER DENGAN MENGGUNAKAN METODE NEWTON-RAPHSON MODIFIKASI FUZZY

Elis Ratna Wulan; Ginanjar Pajarudin; Dian Nuraiman

SOLUSI NUMERIK PERSAMAAN NON-LINIER DENGAN MENGGUNAKAN METODE NEWTON-RAPHSON MODIFIKASI FUZZY

Elis Ratna Wulan^(1*), Ginanjar Pajarudin⁽²⁾, Dian Nuraiman⁽³⁾

(1) Jurusan Matematika,Fakultas Sains dan Teknologi, Indonesia
(2) Jurusan Matematika,Fakultas Sains dan Teknologi, Indonesia
(3) Jurusan Matematika,Fakultas Sains dan Teknologi, Indonesia
(*) Corresponding Author

Abstract

Persamaan non-linear merupakan salah satu kajian dalam ilmu matematika.
Beberapa metode numerik telah dikembangkan untuk menyelesaikan persamaan non
linear. Metode yang digunakan pada penelitian ini adalah metode Newton Raphson
Modifikasi Fuzzy. Untuk menghindari perhitungan �′(��) = 0 diterapkan
modifikasi metode Newton-Raphson, dengan mengganti �′(��) dalam formula
Newton Raphson menggunakan tabel interpolasi, di mana interpolasi ditulis dalam
bentuk Newtonian. Kemudian dapat dihitung nilai taksiran untuk �(��)
menggunakan interpolasi Newton. Metode penyelesaian persamaan non linear ini
akan dibahas pada contoh studi kasus. Persamaan Non Linier yang digunakan pada
penelitian ini adalah � [�1, �2, �3] = [3,4,5] [�1, �2, �3]2 −
[1,2,3] [�1, �2, �3] + [1,2,3] dengan menggunakan metode Newton Raphson
modifikasi Fuzzy diperoleh nilai taksiran untuk �[3,4,5] =
[−5,57.99999959,184.3059112].

Keywords

Bilangan Segitiga Fuzzy; Persamaan Non Linear; Metode Newton Raphson; Metode Secant; Interpolasi.

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