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New Optimal Newton-Householder Methods for Solving Nonlinear Equations and Their Dynamics 被引量:3
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作者 Syahmi Afandi Sariman Ishak Hashim 《Computers, Materials & Continua》 SCIE EI 2020年第10期69-85,共17页
The classical iterative methods for finding roots of nonlinear equations,like the Newton method,Halley method,and Chebyshev method,have been modified previously to achieve optimal convergence order.However,the Househo... The classical iterative methods for finding roots of nonlinear equations,like the Newton method,Halley method,and Chebyshev method,have been modified previously to achieve optimal convergence order.However,the Householder method has so far not been modified to become optimal.In this study,we shall develop two new optimal Newton-Householder methods without memory.The key idea in the development of the new methods is the avoidance of the need to evaluate the second derivative.The methods fulfill the Kung-Traub conjecture by achieving optimal convergence order four with three functional evaluations and order eight with four functional evaluations.The efficiency indices of the methods show that methods perform better than the classical Householder’s method.With the aid of convergence analysis and numerical analysis,the efficiency of the schemes formulated in this paper has been demonstrated.The dynamical analysis exhibits the stability of the schemes in solving nonlinear equations.Some comparisons with other optimal methods have been conducted to verify the effectiveness,convergence speed,and capability of the suggested methods. 展开更多
关键词 Iterative method householder method simple root optimal convergence nonlinear equation
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Hybrid Steffensen’s Method for Solving Nonlinear Equation
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作者 Hamideh Eskandari 《Applied Mathematics》 2022年第9期745-752,共8页
In this paper, we are going to present a class of nonlinear equation solving methods. Steffensen’s method is a simple method for solving a nonlinear equation. By using Steffensen’s method and by combining this metho... In this paper, we are going to present a class of nonlinear equation solving methods. Steffensen’s method is a simple method for solving a nonlinear equation. By using Steffensen’s method and by combining this method with it, we obtain a new method. It can be said that this method, due to not using the function derivative, would be a good method for solving the nonlinear equation compared to Newton’s method. Finally, we will see that Newton’s method and Steffensen’s hybrid method both have a two-order convergence. 展开更多
关键词 CONVERGENCE simple root Newton’s Method Steffensen’s Method Nonlinear Equation Iteration Method Steffensen’s Hybrid Method
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