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AIMS Mathematics

2023, Volume 8, Issue 9: 22371-22384. doi: 10.3934/math.20231141
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Research article

Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems

  • School of Mathematical Sciences, Bohai University, Jinzhou 121000, China
  • Received: 03 June 2023 Revised: 08 July 2023 Accepted: 11 July 2023 Published: 13 July 2023

  • MSC : 49M15, 65J15, 65G99

  • In this paper, the semilocal convergence of the eighth order iterative method is proved in Banach space by using the recursive relation, and the proof process does not need high order derivative. By selecting the appropriate initial point and applying the Lipschitz condition to the first order Fréchet derivative in the whole region, the existence and uniqueness domain are obtained. In addition, the theoretical results of semilocal convergence are applied to two nonlinear systems, and satisfactory results are obtained.

    Citation: Xiaofeng Wang, Yufan Yang, Yuping Qin. Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems[J]. AIMS Mathematics, 2023, 8(9): 22371-22384. doi: 10.3934/math.20231141

    Related Papers:

  • In this paper, the semilocal convergence of the eighth order iterative method is proved in Banach space by using the recursive relation, and the proof process does not need high order derivative. By selecting the appropriate initial point and applying the Lipschitz condition to the first order Fréchet derivative in the whole region, the existence and uniqueness domain are obtained. In addition, the theoretical results of semilocal convergence are applied to two nonlinear systems, and satisfactory results are obtained.


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