CMMSE: Jacobian-free vectorial iterative scheme to find several
solutions simultaneously
- Paula Triguero-Navarro
, - Alicia Cordero
, - Juan Ramon Torregrosa
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Alicia Cordero
![](https://d197for5662m48.cloudfront.net/assets/icons/omniauth/orcid-ca37582cd91a671ed5cec57770e0e96c01b4b79b8b5b75d8598fc1ddac18c974.svg)
Universitat Politecnica de Valencia Institut de Matematica Multidisciplinar
Author ProfileJuan Ramon Torregrosa
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Universitat Politecnica de Valencia Institut de Matematica Multidisciplinar
Author ProfileAbstract
This manuscript is devoted to a derivative-free parametric iterative
step to obtain roots simultaneously for both nonlinear systems and
equations. We prove that when it is added to an arbitrary scheme, it
doubles the convergence order of the original procedure and defines a
new algorithm that obtains several solutions simultaneously. Different
numerical experiments are carried out to check the behaviour of the
iterative methods by changing the value of the parameter and the initial
guesses. Also, it is perform a numerical example where the dynamical
planes are carried out to see and compare the basins of attraction.14 Sep 2023Submitted to Mathematical Methods in the Applied Sciences 15 Sep 2023Submission Checks Completed
15 Sep 2023Assigned to Editor
22 Sep 2023Review(s) Completed, Editorial Evaluation Pending
03 Oct 2023Reviewer(s) Assigned
19 Feb 2024Editorial Decision: Revise Major
23 Mar 2024Submission Checks Completed
23 Mar 2024Assigned to Editor
23 Mar 2024Review(s) Completed, Editorial Evaluation Pending
04 Apr 2024Reviewer(s) Assigned
17 Jun 2024Review(s) Completed, Editorial Evaluation Pending
20 Jun 2024Reviewer(s) Assigned