HASIL PERBANDINGAN METODE IMPROVED NEWTON-RAPHSON BERBASIS DEKOMPOSISI ADOMIAN DAN BEBERAPA METODE KLASIK PADA MASALAH PERSAMAAN NON-LINIER

Indah Jumawanti, Sutrisno Sutrisno, Bayu Surarso


DOI: https://doi.org/10.14710/jfma.v1i1.8

Abstract


In this paper, we work with ten nonlinear equations to compare a new method in nonlinear equation solving, Improved Newton-Raphson based on Adomian Decomposition method (INR-ADM) that consisting of two types called INR-ADM 1 and INR-ADM 2. The difference between INR-ADM 1 and INR-ADM 2 is on the iteration formula form. From our results, it was showed that INR-ADM 1 and INR-ADM 2 are not always better than classic Newton-Raphson method in term of the iteration number. However, if INR-ADM 1 and INR-ADM 2 are compared to Regula False method and Secant method, they are always better i.e. they had fewer number of iteration. The INR-ADM 1 and INR-ADM 2 had shorter computational time than Regula False method. Furthermore, the computational time of INR-ADM 1 and INR-ADM 2 cannot be claimed that they had shorter or longer if they are compared to Newton-Raphson method and Secant method.


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References


G. Adomian, Nonlinear Stochastic Systems and Applications to Physics, Dorerecht: Kluwer Academic Publishers, 1989.

G. Adomian, Solving Frontier Problems of Physics : The Decomposition Method, Dorerecht: Kluwer Academic Publishers, 1994.

G. Adomian dan R.Rach, “On the solution of algebraic equations by the decomposition method,” J. Math. Anal. Appl., vol. 105, pp. 141-166, 1985.

E. Babolian dan J. Biazar, “Solution of Nonlinear Equations by Modified Adomian Decomposition Method,” Applied Mathematics and Computation, vol. 132, pp. 167-172, 2002.

K. Abbaoui dan J. Cherruault, “Convergence of adomian's method applied to non-linear equations,” Applied Mathematics and Computation, vol. 20, pp. 69-73, 1994.

K. A. a. Y. Cherruault, “Solution of a system of nonlinear equations by Adomian decomposition method,” Applied Mathematics and Computation, vol. 150, pp. 847-854, 2004.

K. Abbaoui dan J. Cherruault, “New ideas for proving convergence of Adomian method,” Comput. Math. Appl., vol. 29, pp. 103-108, 1995.

Y. Cherruault, “Convergence of Adomian's Method,” Math. Comput. Modelling, vol. 14, pp. 83-86, 1990.

Y. Cherruault dan G. Adomian, “Decomposition methods : A new proof of convegence,” Math. Comput. Modelling , vol. 18, pp. 103-106, 1993.

K. S. Min, “Improvements in Newton-Raphson Using Adomian Decomposition Method for Solving Nonlinear Equations,” International Journal of Mathematical Analysis, pp. 1919-1928, 2015.


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