MENENTUKAN AKAR PERSAMAAN NONLINIER DENGAN METODE APPROKSIMASI LINGKARAN

Authors

  • Fadli Frayudi
  • Susila Bahri
  • Nova Noliza Bakar

DOI:

https://doi.org/10.25077/jmu.4.2.38-45.2015

Abstract

Penelitian ini bertujuan untuk menentukan akar dari suatu persamaaan nonlinier dengan menggunakan Metode Approksimasi Lingkaran. Dengan menggunakan metode ini, akar dari persamaan nonlinier dapat ditemukan melalui dua pendekatan, yaitu Teknik Singgung Luar Lingkaran dan Teknik Perpotongan Ortogonal Lingkaran. Misalkan x0 adalah taksiran awal untuk akar persamaan f(x) = 0, kemudian asumsikan x1 = x0 +h dimana h adalah bilangan positif atau negatif kecil. Pada kasus pertama, sebuah lingkaran C1 dengan jari-jari f(x0) digambarkan dengan pusat pada sebarang titik (x0, f(x0)) terhadap kurva fungsi f(x). Lingkaran yang lainnya yaitu C2 dengan jari-jari f(x0 + h) dan pusat pada (x0 + h, f(x0 + h)), digambarkan terhadap kurva fungsi f(x) sedemikian sehingga menyinggung atau berpotongan dengan lingkaran C1 secara eksternal atau ortogonal. Pada kasus yang kedua, sebuah lingkaran C1 dengan jari-jari f(x0+h) digambarkan dengan titik pusat (x0+h, f(x0+h)) terhadap kurva fungsi f(x). Lingkaran yang lainnya yaitu C2 dengan jari-jari f(x0−h) dan pusat pada(x0−h, f(x0−h)) digambarkan terhadap kurva fungsi f(x) sedemikian sehingga menyinggung atau berpotongan dengan lingkaran C1 secara eksternal atau ortogonal. Proses iterasi pada kedua kasus tersebut bergantung pada nilai taksiran awal (x0) yang diambil, semakin dekat nilai taksiran awal yang diambil dengan akar sejatinya, maka akan semakin cepat proses iterasi dalam menentukan akar dari persamaan nonlinier yang diinginkan.

Kata Kunci: Persamaan Nonlinier, Teknik Singgung Luar Lingkaran, Teknik Perpotongan Ortogonal Lingkaran, Metode Approksimasi Lingkaran

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Published

26-07-2019

Issue

Vol. 4 No. 2 (2015)

Section

Articles

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