Selected Papers from the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM)

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

Deadline for manuscript submissions: 30 September 2024 | Viewed by 15935

Special Issue Editors

1. Laboratory of Applied Mathematics for Solving Interdisciplinary Problems of Energy Production, Ulyanovsk State Technical University, Severny Venetz Street 32, 432027 Ulyanovsk, Russia
2. Digital Industry REC, South Ural State University, 76, Lenin Avenue, 454080 Chelyabinsk, Russia
3. Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece
Interests: numerical analysis; scientific computing; applied numerical analysis; computational chemistry; computational material sciences; computational physics; parallel algorithm and expert systems
Special Issues, Collections and Topics in MDPI journals
General Department, National & Kapodistrian University of Athens, Euripus Campus, 34400 Psachna, Greece
Interests: numerical optimization; numerical mathematics; numerical methods; scientific computing; mathematical computing; computational mathematics; numerical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The aim and scope of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) (www.icnaam.org) is to bring together leading scientists of the international numerical and applied mathematics community and to attract original research papers of high quality.

The conference covers all the areas of applied mathematics and numerical analysis. Special attention will also be given to the applications of numerical analysis and mathematics to real-world problems, as well as to important areas of science, technology, medicine, biology, and engineering.

ICNAAM will also give attention to educational tools as well as software for applied mathematics and numerical analysis.

Prof. Dr. Theodore E. Simos
Prof. Dr. Charalampos Tsitouras
Guest Editors

Manuscript Submission Information

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Keywords

  • numerical analysis
  • computational mathematics
  • applied and industrial mathematics
  • scientific computing and algorithms
  • approximation
  • mathematical physics
  • mathematical chemistry
  • mathematical biology and mathematical medicine
  • optimization and operational research
  • discrete applied mathematics
  • mathematical modeling
  • neural networks
  • machine learning

Published Papers (11 papers)

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Research

32 pages, 991 KiB  
Article
A New Methodology for the Development of Efficient Multistep Methods for First-Order IVPs with Oscillating Solutions
by Theodore E. Simos
Mathematics 2024, 12(4), 504; https://doi.org/10.3390/math12040504 - 06 Feb 2024
Viewed by 460
Abstract
In this research, we provide a novel approach to the development of effective numerical algorithms for the solution of first-order IVPs. In particular, we detail the fundamental theory behind the development of the aforementioned approaches and show how it can be applied to [...] Read more.
In this research, we provide a novel approach to the development of effective numerical algorithms for the solution of first-order IVPs. In particular, we detail the fundamental theory behind the development of the aforementioned approaches and show how it can be applied to the Adams–Bashforth approach in three steps. The stability of the new scheme is also analyzed. We compared the performance of our novel algorithm to that of established approaches and found it to be superior. Numerical experiments confirmed that, in comparison to standard approaches to the numerical solution of Initial Value Problems (IVPs), including oscillating solutions, our approach is significantly more effective. Full article
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10 pages, 262 KiB  
Article
On Reusing the Stages of a Rejected Runge-Kutta Step
by Vladislav N. Kovalnogov, Ruslan V. Fedorov, Tamara V. Karpukhina, Theodore E. Simos and Charalampos Tsitouras
Mathematics 2023, 11(11), 2589; https://doi.org/10.3390/math11112589 - 05 Jun 2023
Cited by 1 | Viewed by 1167
Abstract
Runge-Kutta (RK) pairs are amongst the most popular methods for numerically solving Initial Value Problems. While using an RK pair, we may experience rejection of some steps through the interval of integration. Traditionally, all of the evaluations are then dropped, and we proceed [...] Read more.
Runge-Kutta (RK) pairs are amongst the most popular methods for numerically solving Initial Value Problems. While using an RK pair, we may experience rejection of some steps through the interval of integration. Traditionally, all of the evaluations are then dropped, and we proceed with a completely new round of computations. In this work, we propose avoiding this waste and continuing by reusing the rejected RK stages. We focus especially on an RK pair of orders six and five. After step rejection, we reuse all the previously evaluated stages and only add three new stages. We proceed by evaluating the output using a smaller step. By this technique, we manage to significantly reduce the cost in a set of problems that are known to pose difficulties in RK algorithms with changing step sizes. Full article
20 pages, 6870 KiB  
Article
Application of Combined Micro- and Macro-Scale Models to Investigate Heat and Mass Transfer through Textile Structures with Additional Ventilation
by Aušra Gadeikytė, Aušra Abraitienė and Rimantas Barauskas
Mathematics 2023, 11(11), 2532; https://doi.org/10.3390/math11112532 - 31 May 2023
Viewed by 940
Abstract
In this study, computational models of heat and mass exchange through textile structures with additional ventilation at the micro- and macro-scale were investigated. The finite element analysis of advanced textile materials provides a better understanding of their heat and mass transfer properties, which [...] Read more.
In this study, computational models of heat and mass exchange through textile structures with additional ventilation at the micro- and macro-scale were investigated. The finite element analysis of advanced textile materials provides a better understanding of their heat and mass transfer properties, which influence thermal comfort. The developed computational models can predict air permeability (AP), thermal resistance (Rct), and heat transfer (h) coefficients at the micro-scale. Moreover, the mesh size was taken into consideration and validated with experimental data presented in the literature. In addition, computational models were extended to micro- and macro-scale forced ventilation models. Macro-scale finite element models require input parameters such as an effective heat transfer coefficient that are usually obtained experimentally. In this research, the heat transfer coefficients (hmicrolayer = 25.603 W/(K·m2), htotal = 8.9646 W/(K·m2)) were obtained numerically from the micro-scale model and were applied to a macro-scale model. The proposed methodology and developed models facilitate the determination of average temperature and temperature distributions through different through-thickness positions along the axis Oz. The simulations were carried out using Comsol Multiphysics and Matlab software. Full article
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13 pages, 1664 KiB  
Article
Computation of Time-Varying {2,3}- and {2,4}-Inverses through Zeroing Neural Networks
by Xingyuan Li, Chia-Liang Lin, Theodore E. Simos, Spyridon D. Mourtas and Vasilios N. Katsikis
Mathematics 2022, 10(24), 4759; https://doi.org/10.3390/math10244759 - 14 Dec 2022
Viewed by 924
Abstract
This paper investigates the problem of computing the time-varying {2,3}- and {2,4}-inverses through the zeroing neural network (ZNN) method, which is presently regarded as a state-of-the-art method for computing the time-varying matrix Moore–Penrose inverse. As a result, two new ZNN models, dubbed ZNN23I [...] Read more.
This paper investigates the problem of computing the time-varying {2,3}- and {2,4}-inverses through the zeroing neural network (ZNN) method, which is presently regarded as a state-of-the-art method for computing the time-varying matrix Moore–Penrose inverse. As a result, two new ZNN models, dubbed ZNN23I and ZNN24I, for the computation of the time-varying {2,3}- and {2,4}-inverses, respectively, are introduced, and the effectiveness of these models is evaluated. Numerical experiments investigate and confirm the efficiency of the proposed ZNN models for computing the time-varying {2,3}- and {2,4}-inverses. Full article
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16 pages, 914 KiB  
Article
Towards Higher-Order Zeroing Neural Network Dynamics for Solving Time-Varying Algebraic Riccati Equations
by Houssem Jerbi, Hadeel Alharbi, Mohamed Omri, Lotfi Ladhar, Theodore E. Simos, Spyridon D. Mourtas and Vasilios N. Katsikis
Mathematics 2022, 10(23), 4490; https://doi.org/10.3390/math10234490 - 28 Nov 2022
Cited by 8 | Viewed by 1215
Abstract
One of the most often used approaches for approximating various matrix equation problems is the hyperpower family of iterative methods with arbitrary convergence order, whereas the zeroing neural network (ZNN) is a type of neural dynamics intended for handling time-varying problems. A family [...] Read more.
One of the most often used approaches for approximating various matrix equation problems is the hyperpower family of iterative methods with arbitrary convergence order, whereas the zeroing neural network (ZNN) is a type of neural dynamics intended for handling time-varying problems. A family of ZNN models that correlate with the hyperpower iterative methods is defined on the basis of the analogy that was discovered. These models, known as higher-order ZNN models (HOZNN), can be used to find real symmetric solutions of time-varying algebraic Riccati equations. Furthermore, a noise-handling HOZNN (NHOZNN) class of dynamical systems is introduced. The traditional ZNN and HOZNN dynamic flows are compared theoretically and numerically. Full article
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24 pages, 1945 KiB  
Article
Research on the Priority of Service Quality Index for Online English Teaching during the COVID-19 Pandemic: Dual Perspective
by Yu-Yu Ma, Jwu-Jenq Chen and Chia-Liang Lin
Mathematics 2022, 10(19), 3642; https://doi.org/10.3390/math10193642 - 05 Oct 2022
Cited by 3 | Viewed by 1190
Abstract
Online English education has become a very common way of educating and learning during the coronavirus pandemic. However, the weight analysis index for the service quality survey of the online English education industry remains a research gap during this period. Thus, this research [...] Read more.
Online English education has become a very common way of educating and learning during the coronavirus pandemic. However, the weight analysis index for the service quality survey of the online English education industry remains a research gap during this period. Thus, this research implemented the analytic network process (ANP) to analyse the index, weight and ranking of online English teaching based on the service quality (SERVQUAL) questionnaire and compare the differences between the dual perspectives of service providers and consumers. Interestingly, this research found that the dimension of responsiveness was considered the most important by service providers. However, consumers deemed the dimension of assurance to be the most significant. Meanwhile, this study discovered that consumers paid more attention to reassurance and safety when they faced problems and transaction procedures during the coronavirus pandemic. In addition, this research found that dimensions utilised to evaluate the quality of online education service are similar whether in the COVID-19 epidemic or prior to the coronavirus pandemic. Thus, it has a certain reference value for evaluating the service quality of online English teaching through the use of dimensions and index weights in the SERVQUAL scale during the coronavirus pandemic. Finally, the findings of this research revealed weights of dimensions and indicators, thereby providing suggestions for maintaining good service quality within online English teaching during the COVID-19 pandemic. Full article
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12 pages, 464 KiB  
Article
Runge–Kutta Embedded Methods of Orders 8(7) for Use in Quadruple Precision Computations
by Vladislav N. Kovalnogov, Ruslan V. Fedorov, Tamara V. Karpukhina, Theodore E. Simos and Charalampos Tsitouras
Mathematics 2022, 10(18), 3247; https://doi.org/10.3390/math10183247 - 07 Sep 2022
Cited by 8 | Viewed by 1638
Abstract
High algebraic order Runge–Kutta embedded methods are commonly used when stringent tolerances are demanded. Traditionally, various criteria are satisfied while constructing these methods for application in double precision arithmetic. Firstly we try to keep the magnitude of the coefficients low, otherwise we may [...] Read more.
High algebraic order Runge–Kutta embedded methods are commonly used when stringent tolerances are demanded. Traditionally, various criteria are satisfied while constructing these methods for application in double precision arithmetic. Firstly we try to keep the magnitude of the coefficients low, otherwise we may experience loss of accuracy; however, when working in quadruple precision we may admit larger coefficients. Then we are able to construct embedded methods of orders eight and seven (i.e., pairs of methods) with even smaller truncation errors. A new derived pair, as expected, is performing better than state-of-the-art pairs in a set of relevant problems. Full article
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13 pages, 896 KiB  
Article
Advances in Parameter Estimation and Learning from Data for Mathematical Models of Hepatitis C Viral Kinetics
by Vladimir Reinharz, Alexander Churkin, Harel Dahari and Danny Barash
Mathematics 2022, 10(12), 2136; https://doi.org/10.3390/math10122136 - 19 Jun 2022
Cited by 2 | Viewed by 1438
Abstract
Mathematical models, some of which incorporate both intracellular and extracellular hepatitis C viral kinetics, have been advanced in recent years for studying HCV–host dynamics, antivirals mode of action, and their efficacy. The standard ordinary differential equation (ODE) hepatitis C virus (HCV) kinetic model [...] Read more.
Mathematical models, some of which incorporate both intracellular and extracellular hepatitis C viral kinetics, have been advanced in recent years for studying HCV–host dynamics, antivirals mode of action, and their efficacy. The standard ordinary differential equation (ODE) hepatitis C virus (HCV) kinetic model keeps track of uninfected cells, infected cells, and free virus. In multiscale models, a fourth partial differential equation (PDE) accounts for the intracellular viral RNA (vRNA) kinetics in an infected cell. The PDE multiscale model is substantially more difficult to solve compared to the standard ODE model, with governing differential equations that are stiff. In previous contributions, we developed and implemented stable and efficient numerical methods for the multiscale model for both the solution of the model equations and parameter estimation. In this contribution, we perform sensitivity analysis on model parameters to gain insight into important properties and to ensure our numerical methods can be safely used for HCV viral dynamic simulations. Furthermore, we generate in-silico patients using the multiscale models to perform machine learning from the data, which enables us to remove HCV measurements on certain days and still be able to estimate meaningful observations with a sufficiently small error. Full article
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13 pages, 906 KiB  
Article
Zeroing Neural Network Approaches Based on Direct and Indirect Methods for Solving the Yang–Baxter-like Matrix Equation
by Wendong Jiang, Chia-Liang Lin, Vasilios N. Katsikis, Spyridon D. Mourtas, Predrag S. Stanimirović and Theodore E. Simos
Mathematics 2022, 10(11), 1950; https://doi.org/10.3390/math10111950 - 06 Jun 2022
Cited by 14 | Viewed by 1501
Abstract
This research introduces three novel zeroing neural network (ZNN) models for addressing the time-varying Yang–Baxter-like matrix equation (TV-YBLME) with arbitrary (regular or singular) real time-varying (TV) input matrices in continuous time. One ZNN dynamic utilizes error matrices directly arising from the equation involved [...] Read more.
This research introduces three novel zeroing neural network (ZNN) models for addressing the time-varying Yang–Baxter-like matrix equation (TV-YBLME) with arbitrary (regular or singular) real time-varying (TV) input matrices in continuous time. One ZNN dynamic utilizes error matrices directly arising from the equation involved in the TV-YBLME. Moreover, two ZNN models are proposed using basic properties of the YBLME, such as the splitting of the YBLME and sufficient conditions for a matrix to solve the YBLME. The Tikhonov regularization principle enables addressing the TV-YBLME with an arbitrary input real TV matrix. Numerical experiments, including nonsingular and singular TV input matrices, show that the suggested models deal effectively with the TV-YBLME. Full article
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13 pages, 2165 KiB  
Article
Relationship of Time-Dependent Parameters from Destructive and Non-Destructive Tests of Structural Concrete
by Petr Lehner and Kristýna Hrabová
Mathematics 2022, 10(3), 460; https://doi.org/10.3390/math10030460 - 30 Jan 2022
Cited by 8 | Viewed by 2790
Abstract
Reinforced concrete structures are typically exposed to a combination of aggressive substances and mechanical stresses, which contribute to fast degradation. The present research was conducted to evaluate five time-dependent parameters from several different tests, namely compressive strength, static modulus, dynamic modulus, surface, and [...] Read more.
Reinforced concrete structures are typically exposed to a combination of aggressive substances and mechanical stresses, which contribute to fast degradation. The present research was conducted to evaluate five time-dependent parameters from several different tests, namely compressive strength, static modulus, dynamic modulus, surface, and bulk electrical resistance. Some parameters were obtained using destructive testing (DT) and some using non-destructive testing (NDT). Due to the correlation and calculation of regression curves, it was possible to compare the correlation of parameters important for estimating the durability of reinforced concrete structures in relation to degradation and corrosion. Concrete of C40/50 grade was examined in several time periods, and the parameter relationships were analysed. At the same time, a statistical evaluation was carried out, and therefore the study contains the average values and standard deviations of all measured parameters. The results show that the compressive strength and the electrical resistivity of the surface and bulk have a high correlation. In contrast, the dynamic modulus and electrical resistivity have low linear correlation, but it was possible to apply a quadratic curve with a high degree of fit. For the comparison of static elastic modulus and electrical resistance, the quality of the quadratic regression model was low but sufficient. The results show that, for structural concrete, the presented NDT methods can be used to estimate other parameters obtained from the DT methods. Full article
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15 pages, 4281 KiB  
Article
Analysis of Measured Parameters in Relation to the Amount of Fibre in Lightweight Red Ceramic Waste Aggregate Concrete
by Marie Horňáková and Petr Lehner
Mathematics 2022, 10(2), 229; https://doi.org/10.3390/math10020229 - 12 Jan 2022
Cited by 9 | Viewed by 1691
Abstract
The present study provides a correlation and regression analysis of lightweight waste aggregate concretes with varying degrees of fibre reinforcement. The concrete mix contains pre-soaked red ceramic waste aggregate, expanded clay coarse aggregate and Portland cement. Copper-coated crimped steel fibre was used as [...] Read more.
The present study provides a correlation and regression analysis of lightweight waste aggregate concretes with varying degrees of fibre reinforcement. The concrete mix contains pre-soaked red ceramic waste aggregate, expanded clay coarse aggregate and Portland cement. Copper-coated crimped steel fibre was used as the reinforcement. The experimental results included properties measured by destructive test methods—compressive strength, splitting tensile strength, static modulus of elasticity, the limit of proportionality, shear strength; and by non-destructive test methods—dynamic modulus of elasticity and surface electrical resistivity. These properties were analysed to study the relevancy and significance between non-destructive and destructive methods of measurement in the case of different amounts of fibre. The results show differences in the degree of fit to the linear and quadratic regression curves for pairs of destructive and non-destructive test results. As expected, the linear relationship can be applied in a few cases, but the quadratic curve must be used for a few pairs. Another observation is that it is not possible to neglect the amount of fibre in the correlation analyses of the measured properties. Full article
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