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Applied Technology with a Modified Sixth-Order Convergent Iterative Method for Solving Nonlinear Equations

Liang Fang, Yun Li, Hai Qun Wang, Rui Chen

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Abstract

With the rapid development and wide applications of information science and applied technology, nonlinear problems become an important direction of research in the field of numerical analysis. In this paper, we mainly study the iterative method for nonlinear equations. We propose and analyze a modified Newton-type method with order of convergence six for solving nonlinear equations. The method is free from second derivatives. The efficiency index of the presented method is 1.565, which is better than that of the classical Newton’s method 1.414. Some numerical experiments illustrate the efficiency and performance of the proposed method.

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What this paper is about

With the rapid development and wide applications of information science and applied technology, nonlinear problems become an important direction of research in the field of numerical analysis. In this paper, we mainly study the iterative method for nonlinear equations. We propose and analyze a modified Newton-type method with order of convergence six for solving nonlinear equations. The method is free from second derivatives. The efficiency index of the presented method is 1.565, which is better than that of the classical Newton’s method 1.414. Some numerical experiments illustrate the efficiency and performance of the proposed method.

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Available abstract

With the rapid development and wide applications of information science and applied technology, nonlinear problems become an important direction of research in the field of numerical analysis. In this paper, we mainly study the iterative method for nonlinear equations. We propose and analyze a modified Newton-type method with order of convergence six for solving nonlinear equations. The method is free from second derivatives. The efficiency index of the presented method is 1.565, which is better than that of the classical Newton’s method 1.414. Some numerical experiments illustrate the efficiency and performance of the proposed method.

Key concepts: Local convergence, Nonlinear system, Convergence (economics), Steffensen's method, Newton's method, Iterative method, Applied mathematics, Secant method

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