Novel Three Order Methods for Solving a System of Nonlinear Equations

Khirallah, M.Q.; Hafiz, M.A.

doi:10.18052/www.scipress.com/BMSA.2.1

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Novel Three Order Methods for Solving a System of Nonlinear Equations

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Abstract:

In this paper, we suggest and study Simpson's formula, and Newton's two, three and four Cosed formulas iterative methods for solving the system of nonlinear equations by using Predictor-Corrector of Newton method. We present four new algorithms for solving the system of nonlinear equations (SNLE). We prove that these new algorithms have convergence. Several numerical examples are given to illustrate the efficiency and performance of the new iterative methods. These new algorithms may be viewed as an extensions and generalizations of the existing methods for solving the system of nonlinear equations.

Info:

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 2)

Pages:

1-12

DOI:

https://doi.org/10.18052/www.scipress.com/BMSA.2.1

Citation:

M.Q. Khirallah and M.A. Hafiz, "Novel Three Order Methods for Solving a System of Nonlinear Equations", Bulletin of Mathematical Sciences and Applications, Vol. 2, pp. 1-12, 2012

Online since:

November 2012

Authors:

M.Q. Khirallah, M.A. Hafiz

Keywords:

Predictor-Corrector Methods, Quadrature Formulas, System of Non-Linear Equations (SNLE)

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Open Access

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Creative Commons Attribution 4.0 International License

References:

M.A. Noor and K.I. Noor, Improved iterative methods for solving nonlinear equations, Appl. Math. Comput. 183, (2006), 774-779.

M.J. Emamzadeh and M.T. Kajani, Nonlinear Fredholm Integral Equation of the Second Kindwith Quadrature Methods , Journal of Mathematical Extension, Vol. 4, No. 2 (2010), 51-58.

S. Abbasbandy, Extended Newton's method for a system of nonlinear equations by modifiedAdomian decomposition method, Appl. Math. Comput. 170, (2005), 648-6567.

H. jafari and V.D. Gejji, Revised Adomian decomposition method for solving a system of nonlinear equations, Appl. Math. Comput. 175, (2006), 1-7.

F. Awawdeh, On new iterative method for solving systems of nonlinear equations. Springer, DOI10. 1007/s11075-009-9342-8.

A.R. Vahidi, Sh. Javadi and S.M. Khorasani, Solving System of Nonlinear Equations by restartedAdomain, s method. Appl. Math. Comput. 6 (2012), 509 -516.

A.R. Soheili, S.A. Ahmadian and J. Naghipoor, A Family of Predictor-Corrector Methods Basedon Weight Combination of Quadratures for Solving Nonlinear Equations, ISSN 17493889, 6 (2008) 29-33 IJNS. (2008). 08. 15/159.

P. Wang, A Third-Order Family of Newton-Like Iteration Methods for Solving Nonlinear Equations Journal of Numerical Mathematics and Stochastics, 3 (1) : 13-19, 2011 , Online: ISSN2151-2302.

M.A. Noor and K.I. Noor, Improved iterative methods for solving nonlinear equations, Appl. Math. Comput. 183, (2006), 774-779.

C. Chun, A new ityerative method for solving nonlinear equations, Appl. Math. Comput. 178(2), (2006), 415-422.

Y.L. Kim, C. Chun and W. Kim, Some Third-order Curvature Based Methods for Solving Nonlinear Equations, Studies in Nonlinear Sciences 1 (3): 72-76, (2010).

M. M. Hosseini and B. Kafash, An Efficient Algorithm for Solving System of Nonlinear Equations, Appl. Math. Sci., 4 (2010), 119 - 131.

M.T. Darvishi and Byeng-Chun Shin, High-Order Newton-Krylov Methods to Solve Systems of Nonlinear Equations. J. KSIAM 15 (2011), 19-30.

M.T. Darvishi, a two-step high order newton-like method for solving systems of nonlinear equations, International Journal of Pure and Applied Mathematics, 57 (2009), 543-555.

M.A. Hafiz, M.S.M. Bahgat, Modified of Householder iterative method for solving nonlinear system of equations. J. Mathematical and Computational Science (2012) (Under Publication).

M.A. Hafiz, M.S.M. Bahgat, An Efficient Two-Step Iterative Method for Solving System of Nonlinear Equations. Journal of Mathematics Research; 4, (4), (2012) 28-34.

M. A. Noor, M. Waseem, K.I. Noor, E. Al-Said, Variational iteration technique for solving a system of nonlinear equations. Optim Lett, (2012), DOI 10. 1007/s11590-012-0479-3.

M.A. Noor, M. Waseem, Some iterative methods for solving a system of nonlinear equations, Computers and Mathematics with Applications 57 (2009) 101-106.

M. T. Darvishi and A. Barati, A third-order Newton-type method to slove systems of nonlinear equations, Appl. Math. Comput. 187, (2007), 630-635.

M. T. Darvishi and A. Barati, Super cubic iterative methods to solve systems nonlinear equations, Appl. Math. Comput. 188, (2007), 1678-1685.

J.H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng. 178(3-4), (1999), 257-262.

A. Golbabai, M. Javidi, A new family of iterative methods for solving system of nonlinear algebric equations, Appl. Math. Comput. 190, (2007), 1717-1722.

M. Ozel: A New Decomposition Method For Solving System Of Nonlinear Equations. Appl. Math. Comput. 15 (2010), 89-95.

J.R. Sharma and R. Sharma, Some Third Order Methods for Solving Systems of Nonlinear Equations, World Academy of Science, Engineering and Technology 60 (2011).

J.L. Hueso, E. Martines and J.R. Torregrosa, Third order iterative methods free from second derivative for nonlinear systems, Applied Mathematics and Computation 215 (2009) 58-65.

R. L. Burden and J. D. Farires, Numerical Analysis,. 9rd ed. Boston, USA, (2011).

M. Podisuk, U. Chundang and W. Sanprasert, Single step formulas and multi-step formulas of the integration method for solving the initial value problem of ordinary differential equation, Applied Mathematics and Computation 190 (2007) 1438-1444.

M.G. Sánchez, Á. Grau and J.L. Díaz-Barrero, on computational order of convergence of some multi-precision solvers of systems of nonlinear equations, arXiv: 1106. 0994v1 [math. NA] 6 Jun (2011).

H.H. Homeier, On Newton-type methods with cubic convergence, Journal of Computational and Applied Mathematics 176 (2005) 425-432.

M.A. Hafiz, M.S.M. Bahgat, extended and modified Halley's iterative method for solving nonlinear system of equations. J. Mathematical and Computational Science (2012) (Under Publication).

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[1] Z. Liu, G. Sun, "Gauss-Legendre Iterative Methods and Their Applications on Nonlinear Systems and BVP-ODEs", Journal of Applied Mathematics and Physics, Vol. 04, p. 2038, 2016

DOI: https://doi.org/10.4236/jamp.2016.411203

[2] H. Srivastava, J. Iqbal, M. Arif, A. Khan, Y. Gasimov, R. Chinram, "A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear Equations", Symmetry, Vol. 13, p. 432, 2021

DOI: https://doi.org/10.3390/sym13030432