Convergence and dynamical study of a new sixth order convergence iterative scheme for solving nonlinear systems

Raudys R. Capdevila; Alicia Cordero; Juan R. Torregrosa; Raudys R. Capdevila; Alicia Cordero; Juan R. Torregrosa

doi:10.3934/math.2023642

AIMS Mathematics

2023, Volume 8, Issue 6: 12751-12777. doi: 10.3934/math.2023642

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Research article

Convergence and dynamical study of a new sixth order convergence iterative scheme for solving nonlinear systems

1.
Institute of Multidisciplinary Mathematics, Universitat Politècnica de València, Valencia, Spain
2.
Colegio Politécnico de Ciencias e Ingeniería, Universidad San Francisco de Quito, Ecuador

Received: 09 December 2022 Revised: 06 March 2023 Accepted: 12 March 2023 Published: 30 March 2023
MSC : 65H10, 37C25

A novel family of iterative schemes to estimate the solutions of nonlinear systems is presented. It is based on the Ermakov-Kalitkin procedure, which widens the set of converging initial estimations. This class is designed by means of a weight function technique, obtaining 6th-order convergence. The qualitative properties of the proposed class are analyzed by means of vectorial real dynamics. Using these tools, the most stable members of the family are selected, and also the chaotical elements are avoided. Some test vectorial functions are used in order to illustrate the performance and efficiency of the designed schemes.
- nonlinear systems of equations,
- iterative scheme,
- convergence order,
- stability,
- chaos,
- efficiency
Citation: Raudys R. Capdevila, Alicia Cordero, Juan R. Torregrosa. Convergence and dynamical study of a new sixth order convergence iterative scheme for solving nonlinear systems[J]. AIMS Mathematics, 2023, 8(6): 12751-12777. doi: 10.3934/math.2023642

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Abstract

A novel family of iterative schemes to estimate the solutions of nonlinear systems is presented. It is based on the Ermakov-Kalitkin procedure, which widens the set of converging initial estimations. This class is designed by means of a weight function technique, obtaining 6th-order convergence. The qualitative properties of the proposed class are analyzed by means of vectorial real dynamics. Using these tools, the most stable members of the family are selected, and also the chaotical elements are avoided. Some test vectorial functions are used in order to illustrate the performance and efficiency of the designed schemes.

References

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