Research Article

Constructing optimal fourth and eighth order iterative methods by using variant of Newton’s method

Abstract

In this paper, we have presented an optimal fourth order iterative method and an optimal eighth order iterative method without memory using weight functions. In terms of computational point of view, our first method require three evaluations (two function and one first derivatives) per iteration to get fourth order and the second method require four evaluations (three functions and one derivatives) per iteration to get eighth order. Hence, these methods have high efficiency indices 1.587 and 1.682 respectively. Some numerical examples are tested to know the performance of the new methods which verifies the theoretical results.

Keywords: Non-linear equation, Multi-point iterations, Optimal order, Kung-Traub conjecture

How to Cite this article: 

Kalyanasundaram Madhu. Constructing optimal fourth and eighth order iterative methods by using variant of Newton’s method. Current Research in Interdisciplinary Studies, 3(3):50-56, 2024. https://doi.org/10.58614/cris333.

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