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Mathematics
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Applications of Symbolic and Soft Computations in Applied Sciences
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Applications of Symbolic and Soft Computations in Applied Sciences

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: closed (30 November 2024) | Viewed by 11114

Special Issue Editors

Dr. Ryszard Walentyński

E-Mail Website
Guest Editor
Department of Civil Engineering, Silesian University of Technology, Gliwice, Poland
Interests: computer algebra systems; computational intelligence; theory of shells; theory of structures; applied and theoretical mechanics
Special Issues, Collections and Topics in MDPI journals
Dr. Rafal Brociek

E-Mail Website
Guest Editor
Department of Artificial Intelligence Modelling, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland
Interests: heat conduction; inverse problem; fractional derivative; intelligent algorithms
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Today’s computing power, together with the wide possibilities offered by various types of computing platforms (such as Wolfram Mathematica, Maxima, Maple, etc.), make the application of symbolic and soft computations in applied sciences and especially engineering very important. Most of the problems in applied sciences can be modeled mathematically. Data for such computation are usually uncertain and fuzzy. On the other hand, formulas for numerical computation should be certain and simple. For solving such problems, symbolic and soft computation, provided by the above-mentioned platforms, are very suitable.

This Special Issue focuses on symbolic soft computations and mathematical algorithms and their application in all kinds of applied scientific and practical problems, such as in engineering, physics, biology, (bio)medicine, economics, etc. The aim is to present different types of applications of mathematical soft computations and the latest achievements in these fields in addition to providing a forum for the exchange of knowledge between people from different fields of science and practice. The scope is focused on the mentioned computational platforms, but not limited to them. It would be very interesting to see the application of optimized algorithms built in these platforms to make the work of the scientist or practitioner more effective and allow focusing the attention on merits.

Prof. Dr. Ryszard Walentyński
Prof. Dr. Rafal Brociek
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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 and soft computations
  • computational intelligence
  • uncertain data
  • mathematical methods
  • algorithms
  • mathematical modeling
  • inverse problems
  • numerical methods
  • optimization

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Published Papers (5 papers)

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Research

13 pages, 727 KiB  
Article
Differential Transform Method and Neural Network for Solving Variational Calculus Problems
by Rafał Brociek and Mariusz Pleszczyński
Mathematics 2024, 12(14), 2182; https://doi.org/10.3390/math12142182 - 11 Jul 2024
Cited by 2 | Viewed by 1386
Abstract
The history of variational calculus dates back to the late 17th century when Johann Bernoulli presented his famous problem concerning the brachistochrone curve. Since then, variational calculus has developed intensively as many problems in physics and engineering are described by equations from this [...] Read more.
The history of variational calculus dates back to the late 17th century when Johann Bernoulli presented his famous problem concerning the brachistochrone curve. Since then, variational calculus has developed intensively as many problems in physics and engineering are described by equations from this branch of mathematical analysis. This paper presents two non-classical, distinct methods for solving such problems. The first method is based on the differential transform method (DTM), which seeks an analytical solution in the form of a certain functional series. The second method, on the other hand, is based on the physics-informed neural network (PINN), where artificial intelligence in the form of a neural network is used to solve the differential equation. In addition to describing both methods, this paper also presents numerical examples along with a comparison of the obtained results.Comparingthe two methods, DTM produced marginally more accurate results than PINNs. While PINNs exhibited slightly higher errors, their performance remained commendable. The key strengths of neural networks are their adaptability and ease of implementation. Both approaches discussed in the article are effective for addressing the examined problems. Full article
(This article belongs to the Special Issue Applications of Symbolic and Soft Computations in Applied Sciences)
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19 pages, 802 KiB  
Article
Fractional-Order SEIRD Model for Global COVID-19 Outbreak
by Rana Yousif, Aref Jeribi and Saad Al-Azzawi
Mathematics 2023, 11(4), 1036; https://doi.org/10.3390/math11041036 - 18 Feb 2023
Cited by 3 | Viewed by 2066
Abstract
With the identification of new mutations in the coronavirus with greater transmissibility and pathogenicity, the number of infected people with COVID-19 worldwide has increased as from 22 June 2021, and a new wave has been created. Since the spread of the coronavirus, many [...] Read more.
With the identification of new mutations in the coronavirus with greater transmissibility and pathogenicity, the number of infected people with COVID-19 worldwide has increased as from 22 June 2021, and a new wave has been created. Since the spread of the coronavirus, many studies have been conducted on different groups. The current research was adopted on the implementations of fractional-order (SEIRD: Susceptible, Exposed, Infected, Recovered, Died) people model with a Caputo derivative for investigating the spread of COVID-19. The characteristics of the system, such as the boundedness, existence, uniqueness and non-negativity of the solutions, the equilibrium points of system, and the basic reproduction number, were analyzed. In the numerical part, a simulation for the spread of the virus is presented, which shows that this wave of spread will continue for the next few months and an increasing number of people becoming infected. Furthermore, the numerical results obtained from several types of fractional-order derivatives are compared with real data, which subsequently shows that the Caputo fractional-order derivative follows real data better than others. In addition, the obtained reproduction number has a value greater than one, indicating a continuation of the disease outbreak and the necessity of taking more control decisions. Full article
(This article belongs to the Special Issue Applications of Symbolic and Soft Computations in Applied Sciences)
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14 pages, 5469 KiB  
Article
Stabilization of Nonlinear Vibration of a Fractional-Order Arch MEMS Resonator Using a New Disturbance-Observer-Based Finite-Time Sliding Mode Control
by Hajid Alsubaie, Amin Yousefpour, Ahmed Alotaibi, Naif D. Alotaibi and Hadi Jahanshahi
Mathematics 2023, 11(4), 978; https://doi.org/10.3390/math11040978 - 14 Feb 2023
Cited by 11 | Viewed by 1922
Abstract
This paper deals with chaos control in an arch microelectromechanical system (MEMS) from the fractional calculus perspective. There is a growing need for effective controllers in various technological fields, and it is important to consider disruptions, uncertainties, and control input limitations when designing [...] Read more.
This paper deals with chaos control in an arch microelectromechanical system (MEMS) from the fractional calculus perspective. There is a growing need for effective controllers in various technological fields, and it is important to consider disruptions, uncertainties, and control input limitations when designing a practical controller. To address this problem, we propose a novel disturbance-observer-based terminal sliding mode control technique for stabilizing and controlling chaos in a fractional-order arch MEMS resonator. The design of this technique takes into account uncertainty, disturbances, and control input saturation in the fractional-order system. The proposed control technique is practical for real-world applications because it includes control input saturation. The equation for a fractional-order arch MEMS resonator is presented, and its nonlinear vibration and chaotic behavior are studied. The design process for the proposed control technique is then described. The Lyapunov stability theorem is used to prove the finite-time convergence of the proposed controller and disturbance observer. The proposed controller is applied to the arch MEMS resonator, and numerical simulations are used to demonstrate its effectiveness and robustness for uncertain nonlinear systems. The results of these simulations clearly show the effectiveness of the proposed control technique. Full article
(This article belongs to the Special Issue Applications of Symbolic and Soft Computations in Applied Sciences)
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8 pages, 1531 KiB  
Article
Estimating the Performance of Computing Clusters without Accelerators Based on TOP500 Results
by Vladimir O. Rybintsev
Mathematics 2022, 10(19), 3580; https://doi.org/10.3390/math10193580 - 30 Sep 2022
Cited by 1 | Viewed by 1368
Abstract
Based on an analysis of TOP500 results, a functional dependence of the performance of clusters without accelerators according to the Linpack benchmark on their parameters was determined. The comparison of calculated and tested results showed that the estimation error does not exceed 2% [...] Read more.
Based on an analysis of TOP500 results, a functional dependence of the performance of clusters without accelerators according to the Linpack benchmark on their parameters was determined. The comparison of calculated and tested results showed that the estimation error does not exceed 2% for processors of different generations and manufacturers (Intel, AMD, Fujitsu) with different technologies of a system interconnect. The achieved accuracy of the calculation allows successful prediction of the performance of a cluster when its parameters (node performance, number of nodes, number of network interfaces, network technology, remote direct memory access, or remote direct memory access over converged Ethernet mode) are changed without resorting to a complex procedure of real testing. Full article
(This article belongs to the Special Issue Applications of Symbolic and Soft Computations in Applied Sciences)
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15 pages, 731 KiB  
Article
Comparison of the Selected Methods Used for Solving the Ordinary Differential Equations and Their Systems
by Edyta Hetmaniok and Mariusz Pleszczyński
Mathematics 2022, 10(3), 306; https://doi.org/10.3390/math10030306 - 19 Jan 2022
Cited by 11 | Viewed by 3114
Abstract
Ordinary differential equations (ODEs), and the systems of such equations, are used for describing many essential physical phenomena. Therefore, the ability to efficiently solve such tasks is important and desired. The goal of this paper is to compare three methods devoted to solving [...] Read more.
Ordinary differential equations (ODEs), and the systems of such equations, are used for describing many essential physical phenomena. Therefore, the ability to efficiently solve such tasks is important and desired. The goal of this paper is to compare three methods devoted to solving ODEs and their systems, with respect to the quality of obtained solutions, as well as the speed and reliability of working. These approaches are the classical and often applied Runge–Kutta method of order 4 (RK4), the method developed on the ground of the Taylor series, the differential transformation method (DTM), and the routine available in the Mathematica software (Mat). Full article
(This article belongs to the Special Issue Applications of Symbolic and Soft Computations in Applied Sciences)
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