Hafizudin Mohamad Nor, A. I. Asnor, Z. R. Yahya, M. Z. Ahmad
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Introduction of Ostrowski Homotopy Continuation Method for Solving Nonlinear Equations Using Mathematica
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.
期刊介绍:
Songklanakarin Journal of Science and Technology (SJST) aims to provide an interdisciplinary platform for the dissemination of current knowledge and advances in science and technology. Areas covered include Agricultural and Biological Sciences, Biotechnology and Agro-Industry, Chemistry and Pharmaceutical Sciences, Engineering and Industrial Research, Environmental and Natural Resources, and Physical Sciences and Mathematics. Songklanakarin Journal of Science and Technology publishes original research work, either as full length articles or as short communications, technical articles, and review articles.