Modifikasi Metode Iterasi Dua Langkah Menggunakan Kombinasi Linear Tiga Parameter Real

Authors

  • Alfi Husni UIN Sultan Syarif Kasim Riau, Indonesia
  • Wartono Wartono UIN Sultan Syarif Kasim Riau, Indonesia

DOI:

https://doi.org/10.33603/e.v6i2.1893

Abstract

Makalah ini membahas modifikasi  metode iterasi dua langkah dengan menggunakan kombinasi linier tiga parameter dan tiga metode iterasi berorde konvergensi tiga yang masing-masing dihasilkan dari penjumlahan metode Potra-Ptak dan metode varian Newton, modifikasi metode varian Newton  rata-rata kontra harmonik, dan Metode Newton-Steffensen. Berdasarkan hasil kajian diperoleh bahwa metode iterasi baru memiliki orde konvergensi empat untuk q 1 = -2, q 2 = 3 - q 3 dan q3 ÎÂ yang melibatkan tiga evaluasi fungsi dengan indeks efisiensi sebesar 41/3 » 1,5874. Simulasi numerik diberikan untuk menunjukkan performa metode iterasi baru dibandingkan dengan metode Newton, metode Potra-Ptak, dan metode Chebyshev

References

Chapra, S. C., dan Canale, R. P., 1998, Numerical Methods for Engineers: with Programming and Software Applications, McGraw-Hill, New York.

Chun, C., 2006, Construction of Newton Like Iteration Methods for Solving Nonlinear Equations, Numerische Mathematik, 104, 297–315.

Chun, C., 2007, A Family of Composite Fourth-Order Iterative Methods for Solving Nonlinear Equations, Applied Mathematics and Computation, 187(2), 951–956.

Chun, C., 2008, A Simply Constructed Third-Order Modifications of Newton's Method, Mathematics and Computation, 219, 81-89.

Ezzati, R., dan Saleki, F., 2011, On the Contruction of New Iterative Methods with Fourth-Order Convergence by Combining Previous Methods, International Mathematical Forum, 6 (27), 1319–1326.

Jisheng, K., Yitian, L., dan Xiuhua, W., 2007, A Composite Fourth-Order Iterative Method for Solving Nonlinear Equations, Applied Mathematics and Computation, 184, 471–475.

Kanwar,V., Singh, S., dan Bakshi, S., 2008, Simple geometric constructions of quadratically and cubically convergent iterative functions to solve nonlinear equations, Numerical Algorithm, 47, 95–107.

Kung, H. T dan Traub, J.F., 1974, Optimal order of one-point and multi-point iteration, Applied Mathematics and Computation, 21, 643 – 651.

Potra, F. A., dan Ptak, V., 1984, Nondiscrete introduction and iterative processes, Research note in Mathematics, 103, Pitman Boston.

Sharma, J. R., 2005, A Composite Third Order Newton-Steffensen Method for Solving Nonlinear Equations, Applied Mathematics and Computation, 169, 242–246.

Traub, J. F., 1964, Iterative Methods for the Solution of Equations, Prentince-Hall,Inc., New York.

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Published

2019-07-26

Issue

Vol. 6 No. 2 (2019): Edisi Juli

Section

Artikel

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