Three-Step Iterative Method with Fifth Order Convergence for Solving Non-linear Equations

Authors

  • Rajesh Kumar Palli Research Scholar, Department of Mathematics GITAM (Deemed to be University), Visakhapatnam, India. Author
  • Mani Sandeep Kumar Mylapalli Department of Mathematics GITAM (Deemed to be University, Visakhapatnam, India. Author
  • Ramadevi Sri Department of Mathematics, Dr. L. Bullayya College, Visakhapatnam, India. Author

DOI:

https://doi.org/10.61841/pyr5a768

Keywords:

Iterative Method, Nonlinear Equation, Newton’s Method, Convergence Analysis

Abstract

In this paper, a new three-step iterative method is proposed based on Newton’s Method to obtain the numerical solution of a non-linear equation. We prove that our method takes over fifth-order convergence, and the efficiency of the recommended method is shown by the numerical examples comparing it with existing methods. 

Downloads

Download data is not yet available.

References

[1] C. Chun, K. Yong-II, “Several new third-order iterative methods for solving nonlinear equations,” Acta Appl. Math., 109 (2010), pp. 1053-1063.

[2] J.R. Sharma, “A composite third order newton-steffensen method for solving nonlinear equations,” Appl. Math. Comput., 169 (2005), pp. 242-246.

[3] Ling Fang, Lisun, Guoping He, “An efficient Newton type method with fifth order convergence for solving nonlinear equations.” Computational and Applied Mathematics, Vol. 27, No. 3 (2008), pp. 269–274.

[4] M.A. Noor, W.A. Khan, K.I. Noor, and E. Al-said, “Higher-order iterative methods free from second-order derivative for solving non-linear equations,” International Journal of Physical Sciences, 6(8) (2011), pp. 1887–1893.

[5] M. Rafiullah Proposed “A fifth-order iterative method to solving nonlinear equations.” Numerical Analysis and Applications, Vol. 4, No. 3 (2011), pp. 239-243.

[6] S. Parimila, M. Kalyanasundaram, and J. Jayakumar. “ Modified Ostrowski Method for Solving Nonlinear Equation.” International Journal of Pure and Applied Mathematics, vol. 120, No. 8 (2018), pp. 59-67.

[7] Zhongyonh Hu, Liu Guocai, and Li Tian, “An iterative method with ninth order convergence for solving nonlinear equations.” Int. J. Contemp. Math. Sciences, Vol. 6, no. 1 (2011), pp. 17-23.

Downloads

Published

31.07.2020

Issue

Vol. 24 No. 5 (2020): 24 (5) 2020

Section

Articles

License

Copyright (c) 2020 AUTHOR

Creative Commons License

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

You are free to:

  1. Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
  2. Adapt — remix, transform, and build upon the material for any purpose, even commercially.
  3. The licensor cannot revoke these freedoms as long as you follow the license terms.

Under the following terms:

  1. Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  2. No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.

Notices:

You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .

No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.

How to Cite

Kumar Palli, R., Sandeep Kumar Mylapalli, M., & Sri , R. (2020). Three-Step Iterative Method with Fifth Order Convergence for Solving Non-linear Equations. International Journal of Psychosocial Rehabilitation, 24(5), 319-324. https://doi.org/10.61841/pyr5a768