New Higher Order Multi-step Methods for Solving Scalar Equations (RETRACTED PAPER)
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Authors
Shin Min Kang
- Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea.
Faisal Ali
- Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan.
Arif Rafiq
- Department of Mathematics and Statistics, Virtual University of Pakistan, Lahore 54000, Pakistan.
Muhammad Asgher Taher
- Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan.
Young Chel Kwund
- Department of Mathematics, Dong-A University, Busan 49315, Korea.
Abstract
We introduce and analyze two new multi-step iterative methods with convergence order four and five
based on modified homotopy perturbation methods, using the system of coupled equations involving an
auxiliary function. We also present the convergence analysis and various numerical examples to demonstrate
the validity and efficiency of our methods. These methods are a good addition and also a generalization of
the existing methods for solving nonlinear equations.
Share and Cite
ISRP Style
Shin Min Kang, Faisal Ali, Arif Rafiq, Muhammad Asgher Taher, Young Chel Kwund, New Higher Order Multi-step Methods for Solving Scalar Equations (RETRACTED PAPER), Journal of Nonlinear Sciences and Applications, 9 (2016), no. 3, 1306--1315
AMA Style
Kang Shin Min, Ali Faisal, Rafiq Arif, Taher Muhammad Asgher, Kwund Young Chel, New Higher Order Multi-step Methods for Solving Scalar Equations (RETRACTED PAPER). J. Nonlinear Sci. Appl. (2016); 9(3):1306--1315
Chicago/Turabian Style
Kang, Shin Min, Ali, Faisal, Rafiq, Arif, Taher, Muhammad Asgher, Kwund, Young Chel. "New Higher Order Multi-step Methods for Solving Scalar Equations (RETRACTED PAPER)." Journal of Nonlinear Sciences and Applications, 9, no. 3 (2016): 1306--1315
Keywords
- Iterative methods
- nonlinear equations
- order of convergence
- auxiliary function
- modified homotopy method.
MSC
References
-
[1]
S. Abbasbandy, Improving Newton-Raphson method for nonlinear equations modified Adomian decomposition method, Appl. Math. Comput., 145 (2003), 887-893.
-
[2]
G. Adomian, Nonlinear Stochastic Systems and Applications to Physics, Kluwer Academic Publishers Group, Dordrecht (1989)
-
[3]
E. Babolian, J. Biazar, Solution of nonlinear equations by modified Adomian decomposition method, Appl. Math. Comput., 132 (2002), 167-172.
-
[4]
C. Chun, Iterative methods improving Newton's method by the decomposition method, Comput. Math. Appl., 50 (2005), 1559-1568.
-
[5]
C. Chun, Y. Ham, A one-parameter fourth-order family of iterative methods for nonlinear equations, Appl. Math. Comput., 189 (2007), 610-614.
-
[6]
V. Daftardar-Gejji, H. Jafari , An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl., 316 (2006), 753-763.
-
[7]
J. H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Engrg., 178 (1999), 257-262.
-
[8]
J. H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Internat. J. Non-Linear Mech., 35 (2000), 37-43.
-
[9]
J. H. He , A new itertration method for solving algebraic equations, Appl. Math. Comput., 135 (2003), 81-84.
-
[10]
J. H. He, The homotopy perturbation method for non-linear oscillators with discontinuities, Appl. Math. Comput., 151 (2004), 287-292.
-
[11]
J. H. He, Asymptotology by homotopy perturbation method , Appl. Math. Comput., 156 (2004), 591-596.
-
[12]
J. H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Soliton Fract., 26 (2005), 695-700.
-
[13]
J. H. He, Limit cycle and bifurcation of nonlinear problems, Chaos Solitons Fractals, 26 (2005), 827-833.
-
[14]
J. H. He, Homotopy perturbation method for solving boundary problems, Phys. Lett. A., 350 (2006), 87-88.
-
[15]
J. H. He, Variational iteration method-some recent results and new interpretations, J. Comput. Appl. Math., 207 (2007), 3-17.
-
[16]
M. Javidi , Fourth-order and fifth-order iterative methods for nonlinear algebraic equations, Math. Comput. Modelling, 50 (2009), 66-71.
-
[17]
M. A. Noor, New classes of iterative methods for nonlinear equations, Appl. Math. Comput., 191 (2007), 128-131.
-
[18]
F. A. Shah, M. A. Noor, Some numerical methods for solving nonlinear equations by using decomposition technique, Appl. Math. Comput., 251 (2015), 378-386.
-
[19]
J. F. Traub, Iterative methods for solution of equations, Chelsea publishing company, New York (1982)