MODIFIKASI SEDERHANA DARI VARIAN METODE NEWTON UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR
Keywords:
Newton’s Method, Secant’s Method, Variant of Newton’s Methods, Nonlinear Equation, Order of Convergence.Abstract
This article discusses a simple modification of the variants of Newton's method for solving nonlinear equations. Jain (2013) combines the use of theSecant method with Trapezoidal Newton's method developed by Weerakon and Fernando (2000) and produces new combination Secant-Trapezoid Newton method that has fourth-order convergence. Using Jain's idea, the authors combine the use of the Secant method with two other variants of Newton's methoddeveloped by Ozban (2004), namely Arithmetic and Harmonic Newton. It turnsout that both the new combinations are has fourth-order convergence. Numericalcalculation with several examples of nonlinear equations is used to show that boththe new combinations method are comparable with other fourth-order methods.References
Atkinson. K.E. (1989). An
Introduction to Numerical
Analysis, second ed. John Wiley
& Sons. New York.
Frontini M. & Sormani E. (2003).
Some variants of Newton’s
method with third-order
convergence, Appl. Math.
Comput. 140, 419–426.
Jain, D. (2013). Family of Newtonlike
methods with fourt-order
convergence. International of
Journal Computer Mathematics.
DOI: 10.1080/
2012.746670.
Mathew, J.H. (1987). Numerical
Method for Mathematical,
Science, and Engineer. Prentice-
Hall Internasional. U.S.A.
Ozban, A.Y. (2004). Some New
Variants of Newton’s Methods.
Applied Mathematics Letters. 17,
-682.
Steffensen, J.F. (1933). Remarks on
iteration. Skand. Aktuarietidskr.
: 64-72.
Supriadi, P. (2013). Metode Secant-
Midpoint Newton untuk
Menyelesaikan Persamaan
Nonlinear. Sedang proses terbit.
Weerakoon, S. & Fernando, T. G. I.
(2000). A variant of Newton’s
Method With Accelerated
Third-Order Convergence.
Applied Mathematics Letters. 13:
–93.
