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

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

*Indah Jumawanti  -  Departemen Matematika, Universitas Diponegoro, Indonesia
Sutrisno Sutrisno  -  Departemen Matematika, Universitas Diponegoro, Indonesia
Bayu Surarso  -  Departemen Matematika, Universitas Diponegoro, Indonesia

Citation Format:
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.

Fulltext View|Download

Article Metrics:

Article Info
Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : ID
Recent articles
OPERATOR ACCRETIVE KUAT PADA RUANG HILBERT PENENTUAN HARGA OPSI DENGAN MODEL BLACK-SCHOLES MENGGUNALKAN METODE BEDA HINGGA FORWARD TIME CENTRAL SPACE ANALISIS BEBERAPA TEOREMA KETUNGGALAN TITIK TETAP DI RUANG METRIK MULTIPLIKATIF (MULTIPLICATIVE METRIC SPACES) More recent articles
  1. G. Adomian, Nonlinear Stochastic Systems and Applications to Physics, Dorerecht: Kluwer Academic Publishers, 1989
  2. G. Adomian, Solving Frontier Problems of Physics : The Decomposition Method, Dorerecht: Kluwer Academic Publishers, 1994
  3. 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
  4. E. Babolian dan J. Biazar, “Solution of Nonlinear Equations by Modified Adomian Decomposition Method,” Applied Mathematics and Computation, vol. 132, pp. 167-172, 2002
  5. 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
  6. 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
  7. K. Abbaoui dan J. Cherruault, “New ideas for proving convergence of Adomian method,” Comput. Math. Appl., vol. 29, pp. 103-108, 1995
  8. Y. Cherruault, “Convergence of Adomian's Method,” Math. Comput. Modelling, vol. 14, pp. 83-86, 1990
  9. Y. Cherruault dan G. Adomian, “Decomposition methods : A new proof of convegence,” Math. Comput. Modelling , vol. 18, pp. 103-106, 1993
  10. K. S. Min, “Improvements in Newton-Raphson Using Adomian Decomposition Method for Solving Nonlinear Equations,” International Journal of Mathematical Analysis, pp. 1919-1928, 2015

Last update:

No citation recorded.

Last update:

No citation recorded.