Solving systems of nonlinear equations using decomposition technique

Subject Areas : History and biography

M. Nili Ahmadabadi ¹ , F. Ahmad ² , G. Yuan ³ , X. Li ⁴

1 - Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Iran
2 - Departament de Fisica i Enginyeria Nuclear, Universitat Politecnica de Catalunya, Comte d'Urgell 187, 08036 Barcelona, Spain
3 - College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P.R. China
4 - School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, Guangxi, China

Received: 2016-07-10 Accepted : 2016-09-20 Published : 2016-09-21

Keywords:

References:

[1] J. M. Ortega, W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, NewYork, 1970.

[2] C. T. Kelley, Solving Nonlinear Equations with Newtons Method, SIAM, Philadelphia, 2003.

[3] F. Ahmad, E. Tohidi, J. A. Carrasco, A parameterized multi-step Newton method for solving systems of nonlinear equations. Numerical Algorithms, (2015), 1017-1398.

[4] F. Ahmad, E. Tohidi, M. Z. Ullah, J. A. Carrasco, Higher order multi-step Jarratt-like method for solving systems of nonlinear equations: Application to PDEs and ODEs, Computers & Mathematics with Applications, 70 (4) (2015), 624-636.

[5] M. Z. Ullah, S. Serra-Capizzano, F. Ahmad, An efficient multi-step iterative method for computing the numerical solution of systems of nonlinear equations associated with ODEs, Applied Mathematics and Computation, 250 (2015), 249-259. 

[6] E. S. Alaidarous, M. Z. Ullah, F. Ahmad, A.S. Al-Fhaid, An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs, Journal of Applied Mathematics, vol. 2013 (2013), Article ID 259371, 11 pages.

[7] F. Ahmed Shah, M, Aslam Noor, Some numerical methods for solving nonlinear equations by using decomposition technique, Appl. Math. Comput. 251 (2015) 378-386.

[8] J. M. Gutirrez, M. A. Hernndez, A family of Chebyshev-Halley type methods in banach spaces, Bull. Aust. Math. Soc. 55 (1997) 113-130.

[9] M. Palacios, Kepler equation and accelerated Newton method, J. Comput. Appl. Math. 138 (2002) 335-346.

[10] S. Amat, S. Busquier, J. M. Gutierrez, Geometrical constructions of iterative functions to solve nonlinear equations. J. Comput. Appl. Math. 157 (2003) 197-205.

[11] M. Frontini, E. Sormani, Some variant of Newtons method with third-order convergence, Appl. Math. Comput. 140 (2003) 419-426.

[12] M. Frontini, E. Sormani, Third-order methods from quadrature formulae for solving systems of nonlinear equations, Appl. Math. Comput. 149 (2004) 771-782.

[13] H. H. H. Homeier, A modified Newton method with cubic convergence: the multivariable case. J. Comput. Appl. Math. 169 (2004) 161-169.

[14] M.T. Darvishi, A. Barati, A fourth-order method from quadrature formulae to solve systems of nonlinear equations. Appl. Math. Comput. 188 (2007) 257-261.

[15] A. Cordero, J.R. Torregrosa, Variants of Newtons method using fifth-order quadrature formulas. Appl. Math. Comput. 190 (2007) 686-698.

[16] M. A. Noor, M. Waseem, Some iterative methods for solving a system of nonlinear equations. Comput. Math. Appl. 57 (2009) 101-106.

[17] M. Grau-Sanchez, A. Grau, M. Noguera, Ostrowski type methods for solving systems of nonlinear equations, Appl. Math. Comput. 218 (2011) 2377-2385.

[18] J.A. Ezquerro, M.Grau-Sanchez, A. Grau, M.A. Hernandez, M. Noguera, N. Romero, On iterative methods with accelerated convergence for solving systems of nonlinear equations, J. Optim. Theory Appl. 151 (2011) 163-174.

[19] A. Cordero, J.L. Hueso, E. Martinez, J.R. Torregrosa, Increasing the convergence order of an iterative method for nonlinear systems, Appl. Math. Lett. 25 (2012) 2369-2374.

[20] J.R. Sharma, R.K. Guha, R. Sharma, An efficient fourth order weighted-Newton method for systems of nonlinear equations, Numer. Algorithms 62 (2013) 307-323.

[21] X. Xiao, H. Yin, A new class of methods with higher order of convergence for solving systems of nonlinear equations, Appl. Math. Comput. 264 (2015) 300-309.

[22] E. D. Dolan and J. J. More, Benchmarking optimization software with performance profiles, Mathematical Programming, 91(2002), 201-213.

[23] V. Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl. 316 (2006) 753-763.

[24] J. H. He, Variational iteration method-some recent results and new interpretations, J. Comput. Appl. Math. 207 (2007) 3-17.

[25] Sergio Amat, Sonia Busquier, ngela Grau, Miquel Grau-Sanchez, Maximum efficiency for a family of Newton-like methods with frozen derivatives and some applications, Applied Mathematics and Computation 219 (2013) 7954-7963.

[26] Xinyuan Wu, Note on the improvement of Newtons method for system of nonlinear equations, Applied Mathematics and Computation. 189 (2007) 1476-1479.