Chalermwut Comemuang, Pairat Janngam อาจารย์สาขาวิชาคณิตศาสตร์ มหาวิทยาลัยราชภัฏบุรีรัมย์ ได้รับการตีพิมพ์วิจัยเรื่อง Sixteenth-Order Iterative Method for Solving Nonlinear Equations ในวารสาร International Journal of Mathematics and Computer Science ระดับ Scopus Quartile 3
Abstract In this paper, we suggest and analyze some new sixteen-order iterative methods by using Householder’s method free from second derivative for solving nonlinear equations. Here we use a new and different technique for implementation of sixteen-order derivative of the function. The efficiency index equals 16^1/6 ≈ 1.587. Numerical examples of the new methods are compared with other methods by exhibiting the effectiveness of the method presented in this paper.
Key words and phrases: Nonlinear equations, Iterative methods, Order of convergence.
Introduction
A common problem in engineering, scientific computing and applied mathematics, in general, is the problem of solving a nonlinear equation f(x) = 0. To find a zero of the non-linear equation, Newton’s method [14] is one of the well known optimal methods using: There exists numerous modifications of the Newton’s method which improve the convergence rate (see [1, 5, 7, 8, 9, 10, 12, 15, 16, 17] and refer
ences therein). For the sake of completeness, we list some existing optimal sixteenth-order convergent methods. In 2011, Geum and Kim [2] proposed a biparametric family of optimally convergent sixteenth-order multipoint methods (GE1): In 2017, Rafiullah and Jabeen [11] proposed Sixteenth Order Iterative Methods (RAF) Our proposed iterative method was developed from a concept of Mylapalli, Palli and Vatti [10] and Householders method [4]. The proposed algorithms are applied to solve some test examples in order to assess its validity
and accuracy.
Convergence Analysis
In this section, we examine a convergence analysis of the newly proposed algorithm in the form of the following theorem:
Theorem 3.1. Suppose that α is a root of the equation f(x) = 0. If f(x) is sufficiently smooth in the neighborhood of α, then the order of convergence of Algorithm 2.3 is sixteen.
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