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Axioms
Special Issues
Iterative Processes for Nonlinear Problems with Applications
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Iterative Processes for Nonlinear Problems with Applications

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (1 November 2021) | Viewed by 12553

Special Issue Editors

Prof. Dr. Juan Ramón Torregrosa Sánchez

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Guest Editor
Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Interests: iterative processes; matrix analysis; numerical analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Alicia Cordero

E-Mail Website
Guest Editor
School of Telecommunications Engineering, Universitat Politècnica de València, 46022 Valencia, Spain
Interests: numerical analysis; iterative methods; nonlinear problems; discrete dynamics; real and complex
Special Issues, Collections and Topics in MDPI journals
Dr. Francisco I. Chicharro

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Guest Editor
Universidad Internacional de La Rioja, Av. La Paz 137, 26006-Logroño, Spain
Interests: iterative methods; fractal dimension; complex dynamics; memory dynamics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Neus Garrido

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Guest Editor
Institute Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain
Interests: numerical analysis; mathematical modelling; numerical modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Different problems in Science and Engineering lack a closed-form solution, mainly nonlinear problems. The direct way is usually not affordable, and efficient algorithms for solving real-world problems have become very important in recent years. These processes are present in artificial intelligence, aerospace communications, or other engineering applications.

The purpose of this Special Issue is to bring together a collection of articles that reflect the latest advances in this field of research. This Special Issue will include (but not be limited to) iterative schemes for solving nonlinear equations and systems or dynamical analysis of iterative methods. In addition, these processes, or others, may be focused on applications such as the aerospace environment (GPS, preliminary orbit determination, etc.), neural networks (CNN, LSTM, etc.), artificial intelligence subprocesses, or chemical applications, amongst others.

Prof. Dr. Juan R. Torregrosa
Prof. Dr. Alicia Cordero
Dr. Francisco I. Chicharro
Dr. Neus Garrido
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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • nonlinear problems
  • iterative methods
  • dynamical analysis
  • GPS procedures
  • optimization
  • machine learning
  • artificial satellites
  • neural networks
  • artificial intelligence

Related Special Issue

Published Papers (5 papers)

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Research

11 pages, 292 KiB  
Article
Semilocal Convergence of the Extension of Chun’s Method
by Alicia Cordero, Javier G. Maimó, Eulalia Martínez, Juan R. Torregrosa and María P. Vassileva
Axioms 2021, 10(3), 161; https://doi.org/10.3390/axioms10030161 - 26 Jul 2021
Cited by 2 | Viewed by 1583
Abstract
In this work, we use the technique of recurrence relations to prove the semilocal convergence in Banach spaces of the multidimensional extension of Chun’s iterative method. This is an iterative method of fourth order, that can be transferred to the multivariable case by [...] Read more.
In this work, we use the technique of recurrence relations to prove the semilocal convergence in Banach spaces of the multidimensional extension of Chun’s iterative method. This is an iterative method of fourth order, that can be transferred to the multivariable case by using the divided difference operator. We obtain the domain of existence and uniqueness by taking a suitable starting point and imposing a Lipschitz condition to the first Fréchet derivative in the whole domain. Moreover, we apply the theoretical results obtained to a nonlinear integral equation of Hammerstein type, showing the applicability of our results. Full article
(This article belongs to the Special Issue Iterative Processes for Nonlinear Problems with Applications)
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10 pages, 256 KiB  
Article
Some New Results on a Three-Step Iteration Process
by Kifayat Ullah, Junaid Ahmad and Manuel de la Sen
Axioms 2020, 9(3), 110; https://doi.org/10.3390/axioms9030110 - 17 Sep 2020
Cited by 5 | Viewed by 2405
Abstract
The purpose of this research work is to prove some weak and strong convergence results for maps satisfying (E)-condition through three-step Thakur (J. Inequal. Appl.2014, 2014:328.) iterative process in Banach spaces. We also present a new example of [...] Read more.
The purpose of this research work is to prove some weak and strong convergence results for maps satisfying (E)-condition through three-step Thakur (J. Inequal. Appl.2014, 2014:328.) iterative process in Banach spaces. We also present a new example of maps satisfying (E)-condition, and prove that its three-step Thakur iterative process is more efficient than the other well-known three-step iterative processes. At the end of the paper, we apply our results for finding solutions of split feasibility problems. The presented research work updates some of the results of the current literature. Full article
(This article belongs to the Special Issue Iterative Processes for Nonlinear Problems with Applications)
18 pages, 345 KiB  
Article
An Accelerated Extragradient Method for Solving Pseudomonotone Equilibrium Problems with Applications
by Nopparat Wairojjana, Habib ur Rehman, Ioannis K. Argyros and Nuttapol Pakkaranang
Axioms 2020, 9(3), 99; https://doi.org/10.3390/axioms9030099 - 17 Aug 2020
Cited by 8 | Viewed by 3041
Abstract
Several methods have been put forward to solve equilibrium problems, in which the two-step extragradient method is very useful and significant. In this article, we propose a new extragradient-like method to evaluate the numerical solution of the pseudomonotone equilibrium in real Hilbert space. [...] Read more.
Several methods have been put forward to solve equilibrium problems, in which the two-step extragradient method is very useful and significant. In this article, we propose a new extragradient-like method to evaluate the numerical solution of the pseudomonotone equilibrium in real Hilbert space. This method uses a non-monotonically stepsize technique based on local bifunction values and Lipschitz-type constants. Furthermore, we establish the weak convergence theorem for the suggested method and provide the applications of our results. Finally, several experimental results are reported to see the performance of the proposed method. Full article
(This article belongs to the Special Issue Iterative Processes for Nonlinear Problems with Applications)
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18 pages, 305 KiB  
Article
Fractional Singular Differential Systems of Lane–Emden Type: Existence and Uniqueness of Solutions
by Yazid Gouari, Zoubir Dahmani, Shan E. Farooq and Farooq Ahmad
Axioms 2020, 9(3), 95; https://doi.org/10.3390/axioms9030095 - 02 Aug 2020
Cited by 9 | Viewed by 2302
Abstract
A coupled system of singular fractional differential equations involving Riemann–Liouville integral and Caputo derivative is considered in this paper. The question of existence and uniqueness of solutions is studied using Banach contraction principle. Furthermore, the question of existence of at least one solution [...] Read more.
A coupled system of singular fractional differential equations involving Riemann–Liouville integral and Caputo derivative is considered in this paper. The question of existence and uniqueness of solutions is studied using Banach contraction principle. Furthermore, the question of existence of at least one solution is discussed. At the end, an illustrative example is given in details. Full article
(This article belongs to the Special Issue Iterative Processes for Nonlinear Problems with Applications)
12 pages, 913 KiB  
Article
Solving a Quadratic Riccati Differential Equation, Multi-Pantograph Delay Differential Equations, and Optimal Control Systems with Pantograph Delays
by Fateme Ghomanjani and Stanford Shateyi
Axioms 2020, 9(3), 82; https://doi.org/10.3390/axioms9030082 - 18 Jul 2020
Cited by 4 | Viewed by 2186
Abstract
An effective algorithm for solving quadratic Riccati differential equation (QRDE), multipantograph delay differential equations (MPDDEs), and optimal control systems (OCSs) with pantograph delays is presented in this paper. This technique is based on Genocchi polynomials (GPs). The properties of Genocchi polynomials are stated, [...] Read more.
An effective algorithm for solving quadratic Riccati differential equation (QRDE), multipantograph delay differential equations (MPDDEs), and optimal control systems (OCSs) with pantograph delays is presented in this paper. This technique is based on Genocchi polynomials (GPs). The properties of Genocchi polynomials are stated, and operational matrices of derivative are constructed. A collocation method based on this operational matrix is used. The findings show that the technique is accurate and simple to use. Full article
(This article belongs to the Special Issue Iterative Processes for Nonlinear Problems with Applications)
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