Version 1
: Received: 10 September 2024 / Approved: 11 September 2024 / Online: 11 September 2024 (14:14:24 CEST)
How to cite:
Cordero, A.; Maimó, J. G.; Rodríguez-Cabral, A.; Torregrosa, A. J. R. Two-Step Fifth-Order Efficient Jacobian-Free Iterative Method for Solving Nonlinear Systems. Preprints2024, 2024090876. https://doi.org/10.20944/preprints202409.0876.v1
Cordero, A.; Maimó, J. G.; Rodríguez-Cabral, A.; Torregrosa, A. J. R. Two-Step Fifth-Order Efficient Jacobian-Free Iterative Method for Solving Nonlinear Systems. Preprints 2024, 2024090876. https://doi.org/10.20944/preprints202409.0876.v1
Cordero, A.; Maimó, J. G.; Rodríguez-Cabral, A.; Torregrosa, A. J. R. Two-Step Fifth-Order Efficient Jacobian-Free Iterative Method for Solving Nonlinear Systems. Preprints2024, 2024090876. https://doi.org/10.20944/preprints202409.0876.v1
APA Style
Cordero, A., Maimó, J. G., Rodríguez-Cabral, A., & Torregrosa, A. J. R. (2024). Two-Step Fifth-Order Efficient Jacobian-Free Iterative Method for Solving Nonlinear Systems. Preprints. https://doi.org/10.20944/preprints202409.0876.v1
Chicago/Turabian Style
Cordero, A., Antmel Rodríguez-Cabral and And Juan R. Torregrosa. 2024 "Two-Step Fifth-Order Efficient Jacobian-Free Iterative Method for Solving Nonlinear Systems" Preprints. https://doi.org/10.20944/preprints202409.0876.v1
Abstract
This article introduces a novel two-step fifth-order Jacobian-free iterative method aimed at efficiently solving systems of nonlinear equations. The method leverages the benefits of Jacobian-free approaches, utilizing divided differences to circumvent the computationally intensive calculation of Jacobian matrices. This adaptation significantly reduces computational overhead and simplifies the implementation process while maintaining high convergence rates. We demonstrate that this method achieves fifth-order convergence under specific parameter settings, with a broad applicability across various types of nonlinear systems. The effectiveness of the proposed method is validated through a series of numerical experiments which confirm its superior performance in terms of accuracy and computational efficiency compared to existing methods.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
