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 2633

Special Issue Editors


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Guest Editor
National Institute of Technology Karnataka, Mangalore 575025, India
Interests: functional analysis; inverse and ill-posed problems; regularization methods; nonlinear analysis; iterative methods
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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

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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://doi.org/10.3390/foundations3040039 - 30 Oct 2023
Viewed by 713
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://doi.org/10.3390/foundations3010003 - 06 Jan 2023
Cited by 1 | Viewed by 1255
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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