Family of Optimal Fourth Order Methods for Multiple Roots and their Dynamics

Authors

  • Prem Bahadur Chand National Academy of Science and Technology, Dhangadhi, Kailali, Nepal
  • Kriti Sethi Guru Tegh Bahadur Institute of Technology, New Delhi, India

DOI:

https://doi.org/10.3126/jnms.v2i2.33005

Keywords:

Non-linear equations, multiple roots, Weerakoon method, Chebyshev method

Abstract

In this paper, we propose a family of fourth order method for solving non-linear equations with multiple roots. The method is based on the arithmetic mean of Weerakoon method and Chebyshev method for multiple roots. Some numerical examples are provided in support of the theoretical results. The numerical results obtained by the method for different values of the parameter are compared with some known methods. The dynamical behaviour of methods is discussed and basins of attraction around the multiple roots for some polynomial is shown at the end of the work.

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Author Biographies

Prem Bahadur Chand, National Academy of Science and Technology, Dhangadhi, Kailali, Nepal

Department of Mathematics, South Asian University, Akbar Bhawan, Chanakya Puri, New Delhi, India

Kriti Sethi, Guru Tegh Bahadur Institute of Technology, New Delhi, India

Department of Mathematics

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Published

2019-12-02

How to Cite

Chand, P. B., & Sethi, K. (2019). Family of Optimal Fourth Order Methods for Multiple Roots and their Dynamics. Journal of Nepal Mathematical Society, 2(2), 1–10. https://doi.org/10.3126/jnms.v2i2.33005

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Section

Articles