Extrapolation-Newton Iterative Solution for Nonlinear Equation

  • Raghad I. Sabri University of Technology
Keywords: Extrapolation method, Newton method, Aitken algorithm.


In this paper, the solution of the nonlinear equation is evaluated using Newton method, and then an extrapolation procedure with Aitken method is applied to improve and accelerated the Newton solution by reducing the number of iterations in order to find the roots of the nonlinear equation with minimum iterations. Several examples are solved using Newton Aitken technique. The comparison based on depending on the number of iterations. 


M. S. Rasheed, An Improved Algorithm For The So lution of Kepler‘s Equation For An Elliptical Orbit, Engineering & Technology Journal, 28 (7) (2010) 1316-1320.

M. S. Rasheed, Acceleration of Predictor Corrector Halley Method in Astrophysics Application, Inter-national Journal of Emerging Technologies in Computational and Applied Sciences, 1 (2) (2012) 91-94.

M. S. Rasheed, On Solving Hyperbolic Trajectory Using New Predictor-Corrector Quadrature Algo-rithms, Baghdad Science Journal, 11 (1) (2014) 186-192.

M. S. Rasheed, Fast Procedure for Solving Two-Body Problem in Celestial Mechanic, Interna-tional Journal of Engineering, Business and Enter-prise Applications, 1 (2) (2012) 60-63.

M. S. Rasheed, Solve the Position to Time Equation for an Object Travelling on a Parabolic Orbit in Ce-lestial Mechanics, DIYALA JOURNAL FOR PURE SCIENCES, 9 (4) (2013) 31-38.

M. S. Rasheed, Approximate Solutions of Barker Equation in Parabolic Orbits, Engineering & Tech-nology Journal, 28 (3) (2010) 492-499.

M. S. Rasheed, Comparison of Starting Values for Im plicit Iterative Solutions to Hyperbolic Orbits Equa-tion, International Journal of Software and Web Sci-ences (IJSWS), 1 (2) (2013) 65-71.

F. Dkhilalli, S. M. Borchani, M. Rasheed, R. Barille, S. Shihab, K. Guidara, M Megdiche, Characteriza-tions and morphology of sodium tungstate particles, Royal Society open science, 5 (8) (2018) 1-16.

F. Dkhilalli, S. Megdiche, K. Guidara, M. Rasheed, R. Barillé, M. Megdiche, AC conductivity evolution in bulk and grain boundary response of sodium tungstate Na2WO4, Ionics, 24 (1) (2018) 169-180.

F. Dkhilalli, S. Megdiche Borchani, M. Rasheed, R. Barille, K. Guidara, M. Megdiche, Structural, die-lectric, and optical properties of the zinc tungstate ZnWO4 compound, Journal of Materials Science: Materials in Electronics, 29 (8) (2018) 6297-6307.

F. Dkhilalli, S. Megdiche Borchani, M. Rasheed, R. Barille, S. Shihab, K. Guidara, M. Megdiche, Char-acterizations and morphology of sodium tungstate particles, Royal Society open science, 5 (8) (2018) 1-12.

M. Enneffati, B. Louati, K. Guidara, M. Rasheed, R. Barillé, Crystal structure characterization and AC electrical conduction behavior of sodium cadmium orthophosphate, Journal of Materials Science: Ma-terials in Electronics, 29 (1) (2018) 171-179.

D. Bouras, A. Mecif, R. Barillé, A. Harabi, M. Rasheed, A. Mahdjoub, M. Zaabat, Cu: ZnO depos-ited on porous ceramic substrates by a simple ther-mal method for photocatalytic application, Ceram-ics International, 44 (17) (2018) 21546-21555.

R. I. Sabri, Solving Nonlinear Equation Using New Iterative Method with Derivative of First Order, Journal of College of Education, 5 (2013) 307-324

R. Villafuerte, J. Medina, R.A.V. S, V. Juárez, M. González, An Iterative Method to Solve Nonlinear Equations, Univers. J. Electr. Electron. Eng. 6 (2019) 14–22.

A. Srivastava, An Iterative Method with Fif-teenth-Order Convergence to Solve Systems of Nonlinear Equations, Comput. Math. Model. 27 (2016) 497–510.

A. Cordero, J.L. Hueso, E. Martínez, J.R. Torregrosa, Multistep High-Order Methods for Nonlinear Equa-tions Using Padé-Like Approximants, Discrete Dyn. Nat. Soc. 2017, (2017) 6.

C. Chun-Mei, F. Gao, A few numerical methods for solving nonlinear equations, International Mathe-matical Forum, 3 (29) (2008) 1437–1443.

R. I. Sabri, A New Three Step Iterative Method with out Second Derivative for Solving Nonlinear Equa-tions, Baghdad Sci. J. 12 (2015) 632–637.

A. Cordero, M.-D. Junjua, J.R. Torregrosa, N. Yas min, F. Zafar, Efficient Four-Parametric with-and-without-Memory Iterative Methods, Pos-sessing High Efficiency Indices, Math. Probl. Eng. 2018 (12) (2018).

R. J. Mitlif, New Iterative Method for Solving Non linear Equations, Baghdad Sci. J. 11 (2014) 1649–1654.

R. I. Sabri, M. N. Mohammed Ali, F. A. Sadak, R. J. Metif, A new Modified Chebyshev's Method with-out second derivative for solving nonlinear equa-tions, Emirates Journal for Engineering Research, 23 (2) (2018) 9-12.

M. S. Rasheed, Modification of Three Order Meth ods for Solving Satellite Orbital Equation in Ellip-tical Motion, Journal of university of Anbar for Pure science, 2019 in press.

E. Kadri, O. Messaoudi, M. Krichen, K. Dhahri, M. Rasheed, E. Dhahri, A. Zouari, K. Khirouni, R. Ba-rillé, Optical and electrical properties of SiGe/Si solar cell heterostructures: Ellipsometric study, Journal of Alloys and Compounds, 721 (2017) 779-783.

E. Kadri, K. Dhahri, A. Zaafouri, M. Krichen, M. Rasheed, K. Khirouni, R. Barillé, Ac conductivity and dielectric behavior of a−Si: H/c− Si1−yGey/p−Si thin films synthesized by molecu-lar beam epitaxial method, Journal of Alloys and Compounds, 705 (2017) 708-713.

M. Rasheed, R. Barillé, Comparison the optical properties for Bi2O3 and NiO ultrathin films depos-ited on different substrates by DC sputtering tech-nique for transparent electronics, Journal of Alloys and Compounds, 728 (2017) 1186-1198.

M. Rasheed, R. Barillé, Optical constants of DC sputtering derived ITO, TiO2 and TiO2: Nb thin films characterized by spectrophotometry and spec-troscopic ellipsometry for optoelectronic devices, Journal of Non-Crystalline Solids, 476 (2017) 1-14.

M. Rasheed, R. Barillé, Room temperature deposi tion of ZnO and Al: ZnO ultrathin films on glass and PET substrates by DC sputtering technique, Optical and Quantum Electronics, 49 (5) (2017) 1-14.

T. Saidani, M. Zaabat, M. S. Aida, R. Barille, M. Rasheed, Y. Almohamed, Influence of precursor source on sol–gel deposited ZnO thin films proper-ties, Journal of Materials Science: Materials in Electronics, 28 (13) (2017) 9252-9257.

E. Kadri, M. Krichen, R. Mohammed, A. Zouari, K. Khirouni, Electrical transport mechanisms in amorphous silicon/crystalline silicon germanium heterojunction solar cell: impact of passivation layer in conversion efficiency, Optical and Quan-tum Electronics, 48 (12) (2016) 1-15.

M. RASHEED, M. A. Sarhan, Characteristics of So lar Cell Outdoor Measurements Using Fuzzy Logic Method, Insight-Mathematics 1 (1) 2019 1-8.

M. RASHEED, M. A. Sarhan, Solve and Implement the main Equations of Photovoltaic Cell Parameters Using Visual Studio Program, Insight-Mathematics 1 (1) 2019 17-29.

M. RASHEED, M. A. Sarhan, Measuring the Solar Cell Parameters Using Fuzzy Set Technique, In-sight-Electronics, 1 (1) (2019) 1-9.

M. RASHEED, Linear Programming for Solving Solar Cell Parameters, Insight-Electronic 1 (1) 2019 10-16.

M. RASHEED, Investigation of Solar Cell Factors using Fuzzy Set Technique, Insight-Electronic 1 (1) 2019 11-17.

M. RASHEED, M. A. Sarhan, Effect of Silicon So lar Cell Physical Factors on Maximum Conversion Efficiency Theoretically and Experimentally, In-sight-Electronic 1 (1) 2019 18-24.