Special Issue "Numerical Analysis and Computational Mathematics"

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

Deadline for manuscript submissions: 30 June 2021.

Special Issue Editors

Dr. Jesús Martín Vaquero
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Guest Editor
Department of Applied Mathematics, Institute of Fundamental Physics and Mathematics, Universidad de Salamanca, Salamanca 37008, Spain
Interests: the development of Runge–Kutta methods for solving nonlinear PDEs; approximation theory and mathematical education based on projects and competencies
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Prof. Dr. Deolinda M. L. Dias Rasteiro
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Guest Editor
Department of Mathematics and Physics, Coimbra Polytechnic—ISEC, Coimbra 3045-093, Portugal
Interests: network optimization; image processing; research on new methods to present mathematics to students
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Prof. Dr. Araceli Queiruga-Dios
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Guest Editor
Department of Applied Mathematics, School of Industrial Engineering, University of Salamanca, Béjar, Salamanca 37700, Spain
Interests: public key cryptography; educational tools and mathematical applications for engineering students
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Dr. Fatih Yilmaz
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Guest Editor
Department of Mathematics, Ankara Hacı Bayram Veli University, Çankaya/Ankara 06570, Turkey
Interests: applications of matrix theory, graph theory, number theory and mathematical education based on projects and competencies
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Special Issue Information

Dear Colleagues,

Mathematical modeling is an active area of applied mathematics. At its beginning, engineers were the main practitioners of this area of mathematics, developing mathematical models to solve engineering problems in natural sciences.

However, analysis methods and models in social sciences are similar to those of nature sciences, including engineering, with the only difference being that instead of using principles of the nature, one uses principles or theories from experts of such social sciences.

Models based on ordinary or partial differential equations describe a wide variety of phenomena such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics, for example. Further, stochastic models have recently received increasing attention. Obviously, some of these types of complex problems also require a deep analysis of the tools utilized to solve these situations.

In this Special Issue, we will attempt to integrate models, methods, and also applications, not only in the scope of traditional natural sciences, but also opening the scope to education and other social sciences. Theory and data-driven models, even in a synergy that gives rise to producing fertile, multidisciplinary, and hybrid models, can be considered. Potential topics include but are not limited to:

  • Numerical and modelling analysis
  • Optimization and evolutionary algorithms models and methods
  • Deterministic differential equations: methods and models
  • Random differential equations: methods and models
  • Numerical solution of large systems of linear and nonlinear equations
  • Educational models and methods
  • Social networks models and methods
  • Engineering models and simulation
  • Analysis modelling in economics and finance
  • Algebraic models and methods with applications
  • Intelligent data analysis models and methods

Before submission, authors should carefully read over the journal’s Author Guidelines, which can be found at: https://www.mdpi.com/journal/axioms/instructions

Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at: https://susy.mdpi.com/  in accordance with the timetable.

Dr. Jesús Martín Vaquero
Prof. Dr. Deolinda M. L. Dias Rasteiro
Dr. Araceli Queiruga-Dios
Dr. Fatih Yılmaz
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 papers will be 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 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 1400 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.

Published Papers (3 papers)

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Research

Open AccessArticle
Approximation Results for Equilibrium Problems Involving Strongly Pseudomonotone Bifunction in Real Hilbert Spaces
Axioms 2020, 9(4), 137; https://doi.org/10.3390/axioms9040137 - 26 Nov 2020
Abstract
A plethora of applications in non-linear analysis, including minimax problems, mathematical programming, the fixed-point problems, saddle-point problems, penalization and complementary problems, may be framed as a problem of equilibrium. Most of the methods used to solve equilibrium problems involve iterative methods, which is [...] Read more.
A plethora of applications in non-linear analysis, including minimax problems, mathematical programming, the fixed-point problems, saddle-point problems, penalization and complementary problems, may be framed as a problem of equilibrium. Most of the methods used to solve equilibrium problems involve iterative methods, which is why the aim of this article is to establish a new iterative method by incorporating an inertial term with a subgradient extragradient method to solve the problem of equilibrium, which includes a bifunction that is strongly pseudomonotone and meets the Lipschitz-type condition in a real Hilbert space. Under certain mild conditions, a strong convergence theorem is proved, and a required sequence is generated without the information of the Lipschitz-type cost bifunction constants. Thus, the method operates with the help of a slow-converging step size sequence. In numerical analysis, we consider various equilibrium test problems to validate our proposed results. Full article
(This article belongs to the Special Issue Numerical Analysis and Computational Mathematics)
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Open AccessArticle
Inertial Iterative Self-Adaptive Step Size Extragradient-Like Method for Solving Equilibrium Problems in Real Hilbert Space with Applications
Axioms 2020, 9(4), 127; https://doi.org/10.3390/axioms9040127 - 31 Oct 2020
Abstract
A number of applications from mathematical programmings, such as minimization problems, variational inequality problems and fixed point problems, can be written as equilibrium problems. Most of the schemes being used to solve this problem involve iterative methods, and for that reason, in this [...] Read more.
A number of applications from mathematical programmings, such as minimization problems, variational inequality problems and fixed point problems, can be written as equilibrium problems. Most of the schemes being used to solve this problem involve iterative methods, and for that reason, in this paper, we introduce a modified iterative method to solve equilibrium problems in real Hilbert space. This method can be seen as a modification of the paper titled “A new two-step proximal algorithm of solving the problem of equilibrium programming” by Lyashko et al. (Optimization and its applications in control and data sciences, Springer book pp. 315–325, 2016). A weak convergence result has been proven by considering the mild conditions on the cost bifunction. We have given the application of our results to solve variational inequality problems. A detailed numerical study on the Nash–Cournot electricity equilibrium model and other test problems is considered to verify the convergence result and its performance. Full article
(This article belongs to the Special Issue Numerical Analysis and Computational Mathematics)
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Open AccessArticle
Application of Bernoulli Polynomials for Solving Variable-Order Fractional Optimal Control-Affine Problems
Axioms 2020, 9(4), 114; https://doi.org/10.3390/axioms9040114 - 13 Oct 2020
Cited by 1
Abstract
We propose two efficient numerical approaches for solving variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann–Liouville integral operator is used in our new techniques. An accurate operational matrix of variable-order fractional [...] Read more.
We propose two efficient numerical approaches for solving variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann–Liouville integral operator is used in our new techniques. An accurate operational matrix of variable-order fractional integration for Bernoulli polynomials is introduced. Our methods proceed as follows. First, a specific approximation of the differentiation order of the state function is considered, in terms of Bernoulli polynomials. Such approximation, together with the initial conditions, help us to obtain some approximations for the other existing functions in the dynamical control-affine system. Using these approximations, and the Gauss—Legendre integration formula, the problem is reduced to a system of nonlinear algebraic equations. Some error bounds are then given for the approximate optimal state and control functions, which allow us to obtain an error bound for the approximate value of the performance index. We end by solving some test problems, which demonstrate the high accuracy of our results. Full article
(This article belongs to the Special Issue Numerical Analysis and Computational Mathematics)
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