A new family of fourth-order Ostrowski-type iterative methods for solving nonlinear systems

Xiaofeng Wang; Mingyu Sun; Xiaofeng Wang; Mingyu Sun

doi:10.3934/math.2024501

AIMS Mathematics

2024, Volume 9, Issue 4: 10255-10266. doi: 10.3934/math.2024501

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Research article

A new family of fourth-order Ostrowski-type iterative methods for solving nonlinear systems

Xiaofeng Wang ^,,
Mingyu Sun

School of Mathematical Sciences, Bohai University, Jinzhou 121000, Liaoning, China

Received: 18 January 2024 Revised: 05 March 2024 Accepted: 07 March 2024 Published: 14 March 2024
MSC : 65B99, 65H05

Ostrowski's iterative method is a classical method for solving systems of nonlinear equations. However, it is not stable enough. In order to obtain a more stable Ostrowski-type method, this paper presented a new family of fourth-order single-parameter Ostrowski-type methods for solving nonlinear systems. As a generalization of the Ostrowski's methods, the Ostrowski's methods are a special case of the new family. It was proved that the order of convergence of the new iterative family was always fourth-order when the parameters take any real number. Finally, the dynamical behavior of the family was briefly analyzed using real dynamical tools. The new iterative method can be applied to solve a wide range of nonlinear equations, and it was used in numerical experiments to solve the Hammerstein equation, boundary value problem, and nonlinear system. These numerical results supported the theoretical results.
- nonlinear systems,
- iterative method,
- stability analysis
Citation: Xiaofeng Wang, Mingyu Sun. A new family of fourth-order Ostrowski-type iterative methods for solving nonlinear systems[J]. AIMS Mathematics, 2024, 9(4): 10255-10266. doi: 10.3934/math.2024501

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Abstract

Ostrowski's iterative method is a classical method for solving systems of nonlinear equations. However, it is not stable enough. In order to obtain a more stable Ostrowski-type method, this paper presented a new family of fourth-order single-parameter Ostrowski-type methods for solving nonlinear systems. As a generalization of the Ostrowski's methods, the Ostrowski's methods are a special case of the new family. It was proved that the order of convergence of the new iterative family was always fourth-order when the parameters take any real number. Finally, the dynamical behavior of the family was briefly analyzed using real dynamical tools. The new iterative method can be applied to solve a wide range of nonlinear equations, and it was used in numerical experiments to solve the Hammerstein equation, boundary value problem, and nonlinear system. These numerical results supported the theoretical results.

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