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Iterative Methods with Applications in Mathematical Sciences II
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Iterative Methods with Applications in Mathematical Sciences II

A special issue of Foundations (ISSN 2673-9321). This special issue belongs to the section "Mathematical Sciences".

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 2707

Special Issue Editors

Prof. Dr. Ioannis K. Argyros

E-Mail Website
Guest Editor
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Interests: numerical analysis; numerical functional analysis; iterative methods for solving equations and systems of equations
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Santhosh George

E-Mail Website
Guest Editor
National Institute of Technology Karnataka, Mangalore 575025, India
Interests: functional analysis; inverse and ill-posed problems; regularization methods; nonlinear analysis; iterative methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Iterative methods are of extreme importance in solving equations and systems of equations, since closed-form solutions can only be found in special cases. The aim of this Special Issue is to present new trends in this area. The topics included in this Special Issue can be any of the following:

  1. Numerical solution of ODE, PDE, and Integral equations;
  2. Variational iterative methods;
  3. Iterative schemes applied to optimization problems;
  4. Design of new Newton-type iterative methods for solving nonlinear equations or systems;
  5. Iterative schemes applied to image processing, radio detection, and ranging;
  6. Iterative schemes for singular problems;
  7. Adomian decomposition methods for non-Newtonian fluids;
  8. Homotopy analysis method for buckling nonuniform columns;
  9. Nonlinear problems associated with automatic guided vehicles;
  10. Variational order fractional financial systems;
  11. Steffensen-type methods for estimating the solution of nonlinear problems;
  12. Variational inequalities in Banach spaces;
  13. Semilocal convergence in Banach spaces;
  14. Generalized equilibrium problems;
  15. Nonlinear models in medicine;
  16. Newton-type methods for differential-algebraic equations and fuzzy integrodifferential equations;
  17. Fixed point theory;
  18. Rocking vibration in geotechnical problems.

Prof. Dr. Ioannis K. Argyros
Prof. Dr. Santhosh George
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Foundations is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • iterative methods
  • fixed point theory
  • convergence of iterative methods
  • optimization
  • variational iterative methods
  • image processing

Published Papers (2 papers)

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Research

17 pages, 567 KiB  
Article
Comparison between Two Competing Newton-Type High Convergence Order Schemes for Equations on Banach Spaces
by Ioannis K. Argyros, Manoj K. Singh and Samundra Regmi
Foundations 2023, 3(4), 643-659; https://0-doi-org.brum.beds.ac.uk/10.3390/foundations3040039 - 30 Oct 2023
Viewed by 739
Abstract
We carried out a local comparison between two ninth convergence order schemes for solving nonlinear equations, relying on first-order Fréchet derivatives. Earlier investigations require the existence as well as the boundedness of derivatives of a high order to prove the convergence of these [...] Read more.
We carried out a local comparison between two ninth convergence order schemes for solving nonlinear equations, relying on first-order Fréchet derivatives. Earlier investigations require the existence as well as the boundedness of derivatives of a high order to prove the convergence of these schemes. However, these derivatives are not in the schemes. These assumptions restrict the applicability of the schemes, which may converge. Numerical results along with a boundary value problem are given to examine the theoretical results. Both schemes are symmetrical not only in the theoretical results (formation and convergence order), but the numerical and dynamical results are also similar. We calculated the convergence radii of the nonlinear schemes. Moreover, we obtained the extraneous fixed points for the proposed schemes, which are repulsive and are not part of the solution space. Lastly, the theoretical and numerical results are supported by the dynamic results, where we plotted basins of attraction for a selected test function. Full article
(This article belongs to the Special Issue Iterative Methods with Applications in Mathematical Sciences II)
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12 pages, 781 KiB  
Article
Improved Higher Order Compositions for Nonlinear Equations
by Gagan Deep and Ioannis K. Argyros
Foundations 2023, 3(1), 25-36; https://0-doi-org.brum.beds.ac.uk/10.3390/foundations3010003 - 06 Jan 2023
Cited by 1 | Viewed by 1288
Abstract
In the present study, two new compositions of convergence order six are presented for solving nonlinear equations. The first method is obtained from the third-order one given by Homeier using linear interpolation, and the second one is obtained from the third-order method given [...] Read more.
In the present study, two new compositions of convergence order six are presented for solving nonlinear equations. The first method is obtained from the third-order one given by Homeier using linear interpolation, and the second one is obtained from the third-order method given by Traub using divided differences. The first method requires three evaluations of the function and one evaluation of the first derivative, thereby enhancing the efficiency index. In the second method, the computation of a derivative is reduced by approximating it using divided differences. Various numerical experiments are performed which demonstrate the accuracy and efficacy of the proposed methods. Full article
(This article belongs to the Special Issue Iterative Methods with Applications in Mathematical Sciences II)
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