Three Step Homotopy Perturbation Iteration Algorithm for Nonlinear Equations

Raghad I. Sabri

Abstract


In this paper, an improved iterative three step method with sixth order convergence based on Homotopy perturbation technique is suggested. It is named three step Homotopy Perturbation iteration algorithm (TSHPI). Four nonlinear test examples are solved with the proposed method and compared to other methods. The obtained results show that TSHPI method is a powerful tool and can generate highly accurate solutions with less iteration.


Full Text:

PDF

Included Database


References


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 Fifteenth-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 Equations Using Padé-Like Approximants, Discrete Dyn. Nat. Soc. (2017).

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

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

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

R. I. Sabri, A New Three Step Iterative Method without Second Derivative for Solving Nonlinear Equations, Baghdad Sci. J. 12 (2015) 632–637.

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. I. Sabri, M. N. Mohammed Ali, F. A. Sadak, R. J. Metif, A new Modified Chebyshev's Method without second derivative for solving nonlinear equations, Emirates Journal for Engineering Research, 23(2) (2018) 9-12.

H. A. Nor , I Arsmah, Newton homotopy solution for nonlinear equations using Maple 14, Journal of Science and Technology, 3(2) (2011).

H. A. Nor, I Arsmah, Numerical solving for nonlinear using higher order homotopy Taylor perturbation, new trends in mathematical sciences, 1(1) (2013).

M. S. Rasheed, An Improved Algorithm For The Solution 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, International 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 Algorithms, Baghdad Science Journal, 11(1) (2014) 186-192.

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

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

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

M. S. Rasheed, Comparison of Starting Values for Implicit Iterative Solutions to Hyperbolic Orbits Equation, International Journal of Software and Web Sciences (IJSWS), 1(2) (2013) 65-71.

Mohammed S. Rasheed, Modification of Three Order Methods for Solving Satellite Orbital Equation in Elliptical Motion, Journal of university of Anbar for Pure science, 2019, in press.

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

N. H. A. Rahman, A. Ibrahim, M. I. Jayes, Newton Homotopy Solution for Nonlinear Equations Using Maple14, J. Sci. Technol. 3 (2011).

N. H. A. Rahman, A. Ibrahim, M. I. Jayes, Numerical solving for nonlinear using higher order homotopy Taylor-perturbation, New Trends Math. Sci. 1 (2013) 24–28.




DOI: https://doi.org/10.18686/esta.v6i2.82

Refbacks

  • There are currently no refbacks.


Copyright (c) 2019 Raghad I. Sabri

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.