Local convergence of a fifth-order Newton-type iterative method for solving systems of nonlinear equations

Le Zhang; Xiaofeng Wang; Le Zhang; Xiaofeng Wang

doi:10.3934/math.2026965

AIMS Mathematics

2026, Volume 11, Issue 8: 23964-23978. doi: 10.3934/math.2026965

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Research article

Local convergence of a fifth-order Newton-type iterative method for solving systems of nonlinear equations

Le Zhang ,
Xiaofeng Wang ^,

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

Received: 27 March 2026 Revised: 17 July 2026 Accepted: 27 July 2026 Published: 05 August 2026
MSC : 65B99, 65H05

Based on the Lipschitz continuity condition, we study the local convergence analysis of a fifth-order Newton-type iterative method to solve nonlinear equations in Banach spaces. Lipschitz continuity condition on the first derivative is assumed to broaden the applicability of the method. Our study provides a thorough local convergence analysis in Banach spaces, including radii of convergence balls, computable error bounds, and the uniqueness of the solution. Finally, numerical experiments on various nonlinear models confirm the theoretical convergence criteria.
- local convergence,
- Banach spaces,
- nonlinear equations,
- radius of convergence,
- iterative method
Citation: Le Zhang, Xiaofeng Wang. Local convergence of a fifth-order Newton-type iterative method for solving systems of nonlinear equations[J]. AIMS Mathematics, 2026, 11(8): 23964-23978. doi: 10.3934/math.2026965

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Abstract

Based on the Lipschitz continuity condition, we study the local convergence analysis of a fifth-order Newton-type iterative method to solve nonlinear equations in Banach spaces. Lipschitz continuity condition on the first derivative is assumed to broaden the applicability of the method. Our study provides a thorough local convergence analysis in Banach spaces, including radii of convergence balls, computable error bounds, and the uniqueness of the solution. Finally, numerical experiments on various nonlinear models confirm the theoretical convergence criteria.

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