Penentuan Akar Persamaan Non Linier Menggunakan Metode Iterasi Tanpa Menghitung Turunan yang Lebih Tinggi

Danisa Olpelda - Universitas Negeri Padang
Muhammad Subhan - Universitas Negeri Padang

Abstract


The iteration method without calculating higher derivatives is one of the numerical methods which is included in the group of open methods. This iteration method is derived based on the third truncated Thiele’s continuous fraction. To avoid calculating higher derivatives, an approximation of the second and third derivatives is used in determining the roots. This research aims to determine the roots of non-linear equations using the iteration method without calculating higher derivatives. This type of research is basic research. Based on the discussion results, it was found that the iteration method without calculating higher derivatives uses two-step in determining the root. The convergence analysis shows that the iteration method without calculating higher derivatives has a convergence order of four. The algorithm of the iteration method without calculating higher derivatives is shown in the form of a flowchart.

Keywords: Non-linear equation, Thiele’s continued fraction, Viscovatov algorithm, iterative method, order of convergence


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DOI: http://dx.doi.org/10.24036/unpjomath.v9i3.16230