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Design of iterative methods with memory for solving nonlinear systems
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  • Alicia Cordero,
  • Neus Garrido,
  • Juan Ramon Torregrosa,
  • Paula Triguero-Navarro
Alicia Cordero
Universidad Politécnica de Valencia

Corresponding Author:[email protected]

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Neus Garrido
Universitat Politecnica de Valencia
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Juan Ramon Torregrosa
Universidad Politécnica de Valencia
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Paula Triguero-Navarro
Universidad Politécnica de Valencia
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In this paper, we design two parametric classes of iterative methods without memory to solve nonlinear systems, whose convergence order is four and seven, respectively. From their error equations and to increase the convergence order without performing new functional evaluations, memory is introduced in these families of different forms. That allows us to increase from four to seven the convergence order in the first family and from seven to eleven in the second one. We perform some numerical experiments with big size systems for confirming the theoretical results and comparing the proposed methods along other known schemes.
04 Sep 2022Submitted to Mathematical Methods in the Applied Sciences
05 Sep 2022Submission Checks Completed
05 Sep 2022Assigned to Editor
19 Sep 2022Reviewer(s) Assigned
06 Jan 2023Review(s) Completed, Editorial Evaluation Pending
18 Jan 2023Editorial Decision: Revise Major
30 Jan 20231st Revision Received
31 Jan 2023Submission Checks Completed
31 Jan 2023Assigned to Editor
31 Jan 2023Review(s) Completed, Editorial Evaluation Pending
10 Feb 2023Reviewer(s) Assigned
18 Feb 2023Editorial Decision: Accept