Browse > Article
http://dx.doi.org/10.7468/jksmeb.2015.22.3.231

NEW FAMILY OF ITERATIVE METHODS FOR SOLVING NON-LINEAR EQUATIONS USING NEW ADOMIAN POLYNOMIALS  

RAFIQ, ARIF (DEPARTMENT OF MATHEMATICS, LAHORE LEADS UNIVERSITY)
PASHA, AYESHA INAM (CIIT)
LEE, BYUNG-SOO (DEPARTMENT OF MATHEMATICS, KYUNGSUNG UNIVERSITY)
Publication Information
The Pure and Applied Mathematics / v.22, no.3, 2015 , pp. 231-243 More about this Journal
Abstract
We suggest and analyze a family of multi-step iterative methods for solving nonlinear equations using the decomposition technique mainly due to Rafiq et al. [13].
Keywords
nonlinear equations; iterative methods; new Adomian polynomials;
Citations & Related Records
연도 인용수 순위
  • Reference
1 C. Chun: Iterative methods improving Newton method by the decomposition method. Comput. Math. Appl. 50 (2005) 1559-1568.   DOI
2 M. Frontini & E. Sormani: Some variants of Newton method with third order convergence. J. Comput. Appl. Math. 140 (2003) 419-426.   DOI
3 J.H. He: A new iteration method for solving algebraic equations. Appl. Math. Comput. 135 (2003) 81-84.   DOI
4 H.H. Homeier: On Newton-type methods with cubic convergence. J. Comput. Appl. Math. 176 (2005) 425-432.   DOI
5 X. Luo: A note on the new iteration for solving algebraic equations. Appl. Math. Comput. 171 (2005) 1177-1183.   DOI
6 M.A. Noor: New family of iterative methods for nonlinear equations. Appl. Math. Comput. 190 (2007) 553-558.   DOI
7 M.A. Noor & K.I. Noor: Some iterative schemes for nonlinear equations. Appl. Math. Comput. 183 (2006) 774-779.   DOI
8 A. Rafiq, B.S. Lee, A.I. Pasha & M.Y. Malik: On Adomian type decomposition method and its convergence. Nonlinear Analysis Forum 16 (2011) 169-181.
9 S. Weerakoon & G.I. Fernando: A variant of Newton method with accelerated third order convergence. Appl. Math. Lett. 17 (2000) 87-93.
10 S. Abbasbandy: Improving Newton Raphson method for nonlinear equations by modified Adomian decomposition method. Appl. Math. Comput. bf 145 (2003) 887-893.   DOI
11 G. Adomian: Nonlinear Stochastic Systems and Applications to Physic. Kluwer Academic Publishers, Dordrecht, 1989.
12 ______: A review of the decomposition method and some recent results for nonlinear equations. Math. Comput. Model 13 (1992), no. 7, 17-43.   DOI
13 ______: Solving Frontier problems of Physics: The Decomposition Method. Kluwer, Boston, MA, 1994.
14 G. Adomian & R. Rach: Noise terms in decomposition series solution. Comput. Math. Appl. 24 (1992), no. 11, 61-64.