Axioms and Methods for Handling Differential Equations and Inverse Problems

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 20 December 2024 | Viewed by 2434

Special Issue Editors


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Guest Editor
1. Department of Environmental Engineering, Faculty of Engineering and Information Technology, University of Pecs, Boszorkany Str. 2, H-7624 Pecs, Hungary
2. Symbolic Methods in Material Analysis and Tomography Research Group, Faculty of Engineering and Information Technology, University of Pecs, Boszorkany Str. 6, H-7624 Pecs, Hungary
Interests: linear differential equations; inverse problems; electrical impedance measurement

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Guest Editor
1. Department of Technical Informatics, Faculty of Engineering and Information Technology, University of Pecs, Boszorkany Str. 6, H-7624 Pecs, Hungary
2. Symbolic Methods in Material Analysis and Tomography Research Group, Faculty of Engineering and Information Technology, University of Pecs, Boszorkany Str. 6, H-7624 Pecs, Hungary
Interests: differential equations; analytical description of patterns of reaction-diffusion systems; chaotic dynamical systems; application of computer algebraic systems in education and research

E-Mail Website
Guest Editor
1. Department of Technical Informatics, Faculty of Engineering and Information Technology, University of Pecs, Boszorkany Str. 6, H-7624 Pecs, Hungary
2. Symbolic Methods in Material Analysis and Tomography Research Group, Faculty of Engineering and Information Technology, University of Pecs, Boszorkany Str. 6, H-7624 Pecs, Hungary
Interests: nonlinear partial differential equations; mathematical biology; mathematical physics

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Guest Editor
1. Institute of Information Technology, University of Dunaujvaros, Tancsics M. Str. 1/A, H-2401 Dunaujvaros, Hungary
2. Symbolic Methods in Material Analysis and Tomography Research Group, Faculty of Engineering and Information Technology, University of Pecs, Boszorkany Str. 6, H-7624 Pecs, Hungary
Interests: robotics; fuzzy control; electrical engineering; optimization methods; electrical impedance tomography; control theory
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
1. Department of Technical Informatics, Faculty of Engineering and Information Technology, University of Pecs, Boszorkany Str. 6, H-7624 Pecs, Hungary
2. Symbolic Methods in Material Analysis and Tomography Research Group, Faculty of Engineering and Information Technology, University of Pecs, Boszorkany Str. 6, H-7624 Pecs, Hungary
Interests: system identification; system dynamics modeling; systems theory; stability analysis; stability modeling; simulation

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Guest Editor
1. John von Neumann Faculty of Informatics, University of Obuda, Becsi ut 96/B., 1034 Budapest, Hungary
2. Institute of Information Technology, University of Dunaujvaros, Tancsics M. Str. 1/A, H-2401 Dunaujvaros, Hungary
Interests: image processing; computer vision; signal processing; electronics; robotics and soft computing methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues:

Modeling real-life problems requires a variety of differential equations that often cause significant challenges for researchers. In the "handling" of these mathematical models, various axioms, mathematical methods, and techniques are able to transform often very complex mathematical objects into a better-behaving representation. The aim of this Special Issue is to collect axioms, mathematical methods, and procedures that are effective for “handling” differential equations even in cases where classical methods have limited or no applications.

For this Special Issue, original research articles, short communications, technical reports, perspectives, extended conference papers, and reviews are welcome. Research areas may include (but are not limited to) the following:

  • Ordinary differential equations;
  • Partial differential equations;
  • Linear differential equations;
  • Nonlinear differential equations;
  • Singular differential equations;
  • Inverse problems;
  • Coefficient inverse problems;
  • Transformations to integral equations.

We look forward to receiving your contributions.

Dr. Zoltán Vizvári
Prof. Dr. Mihály Klincsik
Prof. Dr. Robert Kersner
Prof. Dr. Peter Odry
Dr. Zoltán Sári
Prof. Dr. Vladimir László Tadić
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

  • symbolic mathematical methods
  • ordinary differential equations
  • partial differential equations
  • singular differential equations
  • non-linear differential equation
  • inverse problems

Published Papers (2 papers)

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Research

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12 pages, 6794 KiB  
Communication
A Comparative Study of the Explicit Finite Difference Method and Physics-Informed Neural Networks for Solving the Burgers’ Equation
by Svetislav Savović, Miloš Ivanović and Rui Min
Axioms 2023, 12(10), 982; https://doi.org/10.3390/axioms12100982 - 18 Oct 2023
Cited by 3 | Viewed by 1717
Abstract
The Burgers’ equation is solved using the explicit finite difference method (EFDM) and physics-informed neural networks (PINN). We compare our numerical results, obtained using the EFDM and PINN for three test problems with various initial conditions and Dirichlet boundary conditions, with the analytical [...] Read more.
The Burgers’ equation is solved using the explicit finite difference method (EFDM) and physics-informed neural networks (PINN). We compare our numerical results, obtained using the EFDM and PINN for three test problems with various initial conditions and Dirichlet boundary conditions, with the analytical solutions, and, while both approaches yield very good agreement, the EFDM results are more closely aligned with the analytical solutions. Since there is good agreement between all of the numerical findings from the EFDM, PINN, and analytical solutions, both approaches are competitive and deserving of recommendation. The conclusions that are provided are significant for simulating a variety of nonlinear physical phenomena, such as those that occur in flood waves in rivers, chromatography, gas dynamics, and traffic flow. Additionally, the concepts of the solution techniques used in this study may be applied to the development of numerical models for this class of nonlinear partial differential equations by present and future model developers of a wide range of diverse nonlinear physical processes. Full article
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Review

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10 pages, 242 KiB  
Review
A Survey on the Oscillation of First-Order Retarded Differential Equations
by Ioannis P. Stavroulakis
Axioms 2024, 13(6), 407; https://doi.org/10.3390/axioms13060407 - 17 Jun 2024
Viewed by 156
Abstract
In this paper, a survey of the most interesting conditions for the oscillation of all solutions to first-order linear differential equations with a retarded argument is presented in chronological order, especially in the case when well-known oscillation conditions are not satisfied. The essential [...] Read more.
In this paper, a survey of the most interesting conditions for the oscillation of all solutions to first-order linear differential equations with a retarded argument is presented in chronological order, especially in the case when well-known oscillation conditions are not satisfied. The essential improvement and the importance of these oscillation conditions is also indicated. Full article
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