Metode Iterasi Tiga Langkah dengan Orde Konvergensi Tujuh

Wartono Wartono, Mayumi Istiqomah

Abstract


Potra-Ptak method and Newton’s variant are one of iteration method which it uses for determine
root of nonlinear similarity with third order convergence. In this Final Task, the writer has done modified
composite of Potra-Ptak method and Newton’s variant by enganging θ1 and θ2 parameter and adding the
third step which approximation fꞌ(zn) using second order Lagrange interpolation. Based on the research
result new iteration method have seventh order convergence with θ1=3 and θ2=−2. Each of iteration needs
four f evaluation function which they are f(xn), fꞌ(xn), f(yn) and f(zn) with efficiency index of 71/4≈1,6265.
Numerical simulation is given to show the performance of composite Potra-Ptak method and Newton’s
variant.
Keywords: composite of potra-ptak method and newton’s variant, efficiency index, Lagrange interpolation,
nonlinear equation, order convergence

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References


C.Chapra, Steven. “Applied Numerical Methods with MATLAB for Engineers and Scientists”. Mc

Graw Hill, Singapore. 2005.

Chun, C.“A simply Constructed Third-Order Modifications of Newton’s Method”,Journal of

Computational and Applied Mathematics. Vol.219, hal.81-89,2008.

Chun, C. “Iterative Methods Improving Newton’s Method by The Decomposition

Method”,Computers & Mathematics with Application. Vol.50, hal.1559-1568,2005.

Dukkipati, R. V.,“Numerical Methods”. New Age International Publishers, New Delhi. 2010.

Ezzati, R. “On The Construction of New Iterative Methods with Fourth-Order Convergence by

Combining Previous Methods”,International Mathematical Forum. Vol.06, hal.1319-1326,2011.

Hasanov, V. I., Ivanov, I. G., dan Nedjibov, G., A new modification of Newton’s method, Applied

Mathematics and Engineering, 27, 278 -286, 2002.

Jisheng, K., dkk., Third-order modification of Newton’s method, Journal of Computation and Applied

Mathematics, 205, 1 – 5, 2007.

Jisheng, Kou.,dkk. “A Composite Fourth-Order Iterative Method for Solving Nonlinear

Equation”,Applied Mathematics and Computation. Vol.10, hal.96-100,2006.

Kalyanasundaram, J. J., Modified Newton's method using harmonic mean for solving

nonlinear equations, IOSR Journal of Mathematics, 7(4), 93- 97, 2013.

Khattri, S.K. “Quadrature Based Optimal Iterative Methods with Applications in High-Precision

Computing”,Meth Apple. Vol.05, hal.592-601,2012.

Nedzhibov, G., On a few iterative methods for solving nonlinear equations. Application of

Mathematics in Engineering and Economics XXVIII, in: Proceeding of the XXVIII Summer school

Sozopol’ 02, pp.1-8, Heron press, Sofia, 2002.

Ozban, A.Y., Some New Variants of Newton’s Method, Applied Mathematics Letter, Vol. 17, hal.

-682, 2004.

Sharma, J. R., A Composite Third Order Newton-Steffensen Method for Solving Nonlinear

Equations, Applied Mathematics and Computation, Vol. 169, No. 1, hal .242-246, 2005.

Wang, X dan L. Liping. “Modified Ostrowski’s Method with Eight-Order Convergence and High

Efficiency Index”,Applied Mathematics Letters. Vol.23, hal.549-554,2010.

Weerakoon, S. dan Fernando, T. G. I., “A Variant of Newton’s Method with Accelerated Third-Order

Convergence”,Applied Mathematics Letters. Vol.13, hal.87-93,2000.

Zhao, Lingling.,dkk. “New Families of Eight-Order Methods with High Efficiency Index for Solving

Nonlinear Equations”,Department of Applied Mathematics. Vol.11, hal.2224-2880,2012.


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