Two new efficient sixth order iterative methods for solving nonlinear equations

Obadah Said Solaiman; Ishak Hashim

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Two new efficient sixth order iterative methods for solving nonlinear equations

机译：两种新的求解非线性方程组的高效六阶迭代方法

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In this paper, we present two new iterative methods, one of them is second derivative free, for solving nonlinear equations. We derive these methods based on the Taylor series expansion and Halley’s method. The convergence analysis of the two methods is discussed. It is established that the new methods have sixth order of convergence. Several numerical examples given show that the new methods are comparable with the well-known existing methods of the same order.

机译：在本文中，我们提出了两种新的迭代方法，其中一种是无二阶导数的，用于求解非线性方程。我们根据泰勒级数展开式和哈雷方法得出这些方法。讨论了两种方法的收敛性分析。确定新方法具有六阶收敛性。给出的几个数值示例表明，新方法与已知的相同顺序的现有方法具有可比性。

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《Journal of King Saud University》 |2019年第4期|共5页
作者
Obadah Said Solaiman; Ishak Hashim;
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中图分类自然科学理论与方法论;
关键词
Root finding methodHalley’s methodNonlinear equationsIterative methodsOrder of convergence;

机译：求根法哈利法非线性方程迭代法收敛阶;

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专利

1. An efficient three-step iterative method with sixth-order convergence for solving nonlinear equations [J] . A. RAFIQ, S. HUSSAIN, F. AHMAD, International journal of computer mathematics . 2007,第3期

机译：求解非线性方程组的六阶收敛有效三步迭代方法
2. Two-step Iterative Methods with Sixth-order Convergence for Solving Nonlinear Equations [J] . R. Thukral British Journal of Mathematics & Computer Science . 2014,第14期

机译：求解非线性方程的六阶收敛两步迭代方法
3. Two-step Iterative Methods with Sixth-orderConvergence for Solving Nonlinear Equations [J] . R. Thukral British Journal of Mathematics Computer Science . 2014,第14期

机译：求解非线性方程组的六阶收敛两步迭代方法
4. A new iterative method with sixth-order convergence for solving nonlinear equations [C] . Han Li International Conference on Advanced Engineering Materials and Technology . 2012

机译：一种新的迭代方法，具有求解非线性方程的第六阶收敛
5. Solving large sparse systems of nonlinear equations and nonlinear least squares problems using tensor methods on sequential and parallel computers*. [D] . Bouaricha, Ali. 1992

机译：在连续和并行计算机上使用张量法来求解非线性方程和非线性最小二乘问题的大型稀疏系统。
6. On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations [O] . Taher Lotfi, Alicia Cordero, Juan R. Torregrosa, -1

机译：基于Bi等人的概论。八阶收敛迭代法求解非线性方程
7. Efficient Three-point Iterative Methods for Solving Nonlinear Equations [O] . Xiaofeng Wang 2015

机译：用于求解非线性方程的高效三点迭代方法

Two new efficient sixth order iterative methods for solving nonlinear equations

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