Introduction of Ostrowski Homotopy Continuation Method for Solving Nonlinear Equations using Mathematica

Authors

  • Hafizudin Mohamad Nor Universiti Malaysia Perlis
  • Asma Izzati Asnor Universiti Sains Malaysia
  • Zainor Ridzuan Yahya Universiti Malaysia Perlis
  • Muhammad Zaini Ahmad Universiti Malaysia Perlis

Keywords:

Nonlinear Equations, Ostrowski Homotopy Continuation Method, Homotopy Function

Abstract

The solution to a nonlinear equation is found in this study by combining a classical and a powerful method. Basically, it is well known that the homotopy continuation method (HCM) is a powerful method that has been used for solving the problem of the classical method. A new approach is introduced in this study which is known as the Ostrowski Homotopy Continuation method (Ostrowski-HCM) with a purpose to overcome the divergence problem that arises from the classical Ostrowski’s method when a bad initial guess is used. To put it simply, when the derivative of a given function at the starting point is equal to zero, the problem arises. As a result, the division by zero renders the scheme invalid. In addition, a mathematical software, Mathematica 7.0, is used to implement the Ostrowski-HCM results. Thus, from the analysis of the results, it is proven that the Ostrowski-HCM is reliable and advantageous for solving the nonlinear equation.

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Published

28-06-2022

How to Cite

Mohamad Nor, H. ., Asnor, A. I. ., Yahya, Z. R. ., & Ahmad, M. Z. . (2022). Introduction of Ostrowski Homotopy Continuation Method for Solving Nonlinear Equations using Mathematica. Journal of Science and Technology, 14(1), 37–43. Retrieved from https://publisher.uthm.edu.my/ojs/index.php/JST/article/view/10099