### Metode Tipe Newton Bebas Turunan untuk Menentukan Akar Persamaan Tak Linier

Engki Putra - Student of Mathematics Department State Universitas Negeri Padang, Indonesia
Muhammad Subhan - Lecturers of Mathematics Department State Universitas Negeri Padang, Indonesia
Yusmet Rizal - Lecturers of Mathematics Department State Universitas Negeri Padang, Indonesia

#### Abstract

Abstract –Newton Method and Potra-Ptak Method are an iterative method which is used for solving nonlinear equation. Both of those method still have low order. Newton Method has second order convergence and Potra-Ptak Method  has third order convergence. It make those method slow in getting  roots approximation.  Therefore, researcher  modify both of those  method use Taylor Series to increase the order of convergence, so we obtain Newton Type  Derivative Free Method. So that, the purpose of this research is finding the roots of nonlinear equations using Derivative Free Newton Type Method, making the algorithm and determining the order of convergence. This research is theoretical research by reviewing relevant theories for solving nonlinear equation. The results of the research are Derivative Free Newton Type Method, algorithm of Derivative Free Newton Type Method, and this method has fifth order convergence.

Keywords – Potra and Ptak Method, Taylor series, Derivative Free, Order of Convergence

PDF

#### References

Sutarno, Heru. 2005. Metode Numerik. Bandung: PT Sinar Baru

Algesindo.

Susila, I nyoman. 1992. Metode Numerik. Bandung: FMIPA ITB.

Kumar, Manoj dkk. 2015. “A New Fifth Order Derivative Free Newton-Type Method for Solving Nonlinear Equations”. Paper. India: Department of Mathematics, Montilal Nehru National Institute of Technology.

Zuhrowardi. 2013. ’’Konvergensi Metode Potra-Ptak dengan Menggunakan Kelengkungan Kurva”. Skripsi. Riau: UIN SUSKA Riau.

Suharyono, Yuzi Andri. 2013.’’Konvergensi Metode Potra-Ptak dengan Menggunakan Interpolasi Kuadratik”. Skripsi. Riau:UIN SUSKA Riau.

Munir, Rinaldi. 2003. Metode Numerik. Bandung: Informatika.

Putra, Engki Mai. 2016. “Metode Tipe Newton Modifikasi Bebas Turunan untuk Menentukan Akar Persamaan Tak Linier”. Skripsi. Padang:Universitas Negeri Padang.

DOI: http://dx.doi.org/10.24036/unpjomath.v4i2.6307