High-order iterations for systems of nonlinear equations

References

• S. Amat, S. Busquier, J.M. Gutiérrez, Geometric constructions of iterative functions to solve nonlinear equations.  J. Comput. Appl. Math. Comput. Appl. Math. 157 (2003), pp. 197–205. doi: 10.1016/S0377-0427(03)00420-5
   Web of Science ®Google Scholar
• A. Cordero, J.L. Hueso, E. Martínez and J.R. Torregrosa, A modified Newton–Jarratt's composition, Numer. Algor. 55 (2010), pp. 87–99. doi: 10.1007/s11075-009-9359-z
   Web of Science ®Google Scholar
• A. Cordero, J.L. Hueso, E. Martínez and J.R. Torregrosa, Increasing the convergence order of an iterative method for nonlinear systems, Appl. Math. Lett. 25 (2012), pp. 2369–2374. doi: 10.1016/j.aml.2012.07.005
   Web of Science ®Google Scholar
• A. Cordero, E. Martínez and J.R. Torregrosa, Iterative methods of order four and five for systems of nonlinear equations, Appl. Math. Comput. 231 (2009), pp. 541–551. doi: 10.1016/j.cam.2009.04.015
   Web of Science ®Google Scholar
• A. Cordero, J.R. Torregrosa and M.P. Vassileva, Pseudocomposition: a technique to design predictor-corrector methods for systems of nonlinear equations, Appl. Math. Comput. 218 (2012), pp. 11496–11504.
   Web of Science ®Google Scholar
• M. Grau-Sánchez and A. Grau, On the computational efficiency index and some iterative methods for solving systems of nonlinear equations, J. Comput. App. Math. 236 (2011), pp. 1259–1266. doi: 10.1016/j.cam.2011.08.008
   Web of Science ®Google Scholar
• M. Grau-Sanchez, A. Grau and M. Noguera, Ostrowski type methods for solving systems of nonlinear equations, Appl. Math. Comput. 218 (2011), pp. 2377–2385.
   Web of Science ®Google Scholar
• P. Jarratt, Some fourth order multipoint iterative methods for solving equations, Math. Comput. 20(95) (1966), pp. 434–437. doi: 10.1090/S0025-5718-66-99924-8
   Web of Science ®Google Scholar
• K. Madhu and J. Jayaraman, Some higher order Newton-Like methods for solving system of nonlinear equations and its applications, Int. J. Appl. Comput. Math. 3(3) (2017), pp. 2213–2230. doi: 10.1007/s40819-016-0234-z
   Google Scholar
• A. Mohsen, A simple solution of the Bratu problem, Comput. Math. Appl. 67 (2014), pp. 26–33. doi: 10.1016/j.camwa.2013.10.003
   Web of Science ®Google Scholar
• F.A. Potra, Nondiscrete Induction and Iterative Processes, Pitman, London, 1984.
   Google Scholar
• J.R. Sharma and H. Arora, On efficient weighted-Newton methods for solving systems of nonlinear equations, Appl. Math. Comput. 222 (2013), pp. 497–506.
   Web of Science ®Google Scholar
• J.R. Sharma and H. Arora, Efficient Jarratt-like methods for solving systems of nonlinear equations, Calcolo 51 (2014), pp. 193–210. doi: 10.1007/s10092-013-0097-1
   Web of Science ®Google Scholar
• J.R. Sharma and P. Gaupta, An efficient fifth order method for solving systems of nonlinear equations, Comput. Math. Appl. 67 (2014), pp. 591–601. doi: 10.1016/j.camwa.2013.12.004
   Web of Science ®Google Scholar
• J.R. Sharma and R.K. Guha, Simple yet efficient Newton-like method for systems of nonlinear equations, Calcolo 53 (2016), pp. 451–473. doi: 10.1007/s10092-015-0157-9
   Web of Science ®Google Scholar
• J.R. Sharma, R.K. Guha and R. Sharma, An efficient fourth-order weighted-Newton method for systems of nonlinear equations, Numer. Algor. 62 (2013), pp. 307–323. doi: 10.1007/s11075-012-9585-7
   Web of Science ®Google Scholar
• X. Wang, A family of Newtion-type iterative methods using some special self-accelerating parameters, Int. J. Comput. Math. 95 (2018), pp. 2112–2127. doi: 10.1080/00207160.2017.1366459
   Web of Science ®Google Scholar
• X. Wang, An Ostrowski-type method with memory using a novel self-accelerating parameters, J. Comput. App. Math. 330 (2018), pp. 710–720. doi: 10.1016/j.cam.2017.04.021
   Web of Science ®Google Scholar
• X. Xiao and H. Yin, A new class of methods with higher order of convergence for solving systems of nonlinear equations, Appl. Math. Comput. 264 (2015), pp. 300–309.
   Web of Science ®Google Scholar
• X. Xiao and H. Yin, A simple and efficient method with high order convergence for solving systems of nonlinear equations, Comput. Appl. Math. 69 (2015), pp. 1220–1231. doi: 10.1016/j.camwa.2015.03.018
   Web of Science ®Google Scholar
• X.Y. Xiao and H.W. Yin, Increasing the order of convergence for iterative methods to solve nonlinear systems, Calcolo 53 (2016), pp. 285–300. doi: 10.1007/s10092-015-0149-9
   Web of Science ®Google Scholar
• T. Zhanlav, O. Chuluunbaatar and V. Ulziibayar, Generating functions method for construction new iterations, Appl. Math. Comput. 315 (2017), pp. 414–423.
   Web of Science ®Google Scholar
• T. Zhanlav, O. Chuluunbaatar and V. Ulziibayar, Necessary and sufficient conditions for the convergence of two- and three-point Newton-type iterations, Comput. Math. Math. Phys. 57 (2017), pp. 1090–1100. doi: 10.1134/S0965542517070120
   Web of Science ®Google Scholar
• T. Zhanlav and I.V. Puzynin, The convergence of iteration based on a continuous analogue of Newton's method, Comput. Math. Math. Phys. 32 (1992), pp. 729–737.
   Web of Science ®Google Scholar