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Mathematics
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Numerical Analysis and Applied Mathematics: Theory, Methods, and Applications
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Numerical Analysis and Applied Mathematics: Theory, Methods, and Applications

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

Deadline for manuscript submissions: 31 October 2026 | Viewed by 1054

Editor

Prof. Dr. Theodore E. Simos

grade E-Mail Website
Guest Editor
1. Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, West Mishref, Mubarak Al-Abdullah 32093, Kuwait
2. 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

Special Issue Information

Dear Colleagues,

This Special Issue aims to present high-quality research contributions arising from ICNAAM 2026, focusing on recent advances in numerical analysis and applied mathematics, with a strong emphasis on computational methods and real-world applications. Topics of interest include, but are not limited to, numerical methods for differential equations, computational linear algebra, optimization techniques, stochastic modeling, numerical methods for dynamical systems, scientific computing, and high-performance computing applications.

The Special Issue also welcomes interdisciplinary contributions that bridge mathematical theory with applications in physics, engineering, data science, biology, and finance. Particular attention will be given to innovative algorithms, rigorous theoretical analysis, and validated numerical experiments demonstrating applicability and efficiency.

The Special Issue seeks to reflect the scientific breadth and quality of ICNAAM, offering a platform for disseminating impactful research to the broader applied mathematics community.

Prof. Dr. Theodore E. Simos
Guest Editor

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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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

  • 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

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Published Papers (2 papers)

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Research

17 pages, 996 KB  
Article
An Explicit Diffusion Operator for High-Order Entropy-Stable Schemes in an Augmented 1D Blood Flow Model
by Carlos A. Vega and Andrés Guerra
Mathematics 2026, 14(16), 2960; https://doi.org/10.3390/math14162960 - 16 Aug 2026
Viewed by 133
Abstract
We propose an entropy-stable numerical scheme for an augmented one-dimensional blood flow model by constructing an explicit diffusion operator independent of the reconstruction method used for the scaled entropy variables. The diffusion term plays an important role in entropy-stable schemes, i.e., schemes satisfying [...] Read more.
We propose an entropy-stable numerical scheme for an augmented one-dimensional blood flow model by constructing an explicit diffusion operator independent of the reconstruction method used for the scaled entropy variables. The diffusion term plays an important role in entropy-stable schemes, i.e., schemes satisfying a discrete entropy inequality. In general, the diffusion operator involves a diffusion matrix that depends on the scaled right eigenvectors and on the reconstruction of the scaled variables. We derive a simple, explicit expression for this operator that avoids computing the full set of scaled eigenvectors. The performance of the scheme is assessed through numerical experiments, focusing on Riemann problems, which confirm its ability to capture shock waves accurately and provide numerical evidence of entropy decay for non-smooth solutions. Full article
(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics: Theory, Methods, and Applications)
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25 pages, 435 KB  
Article
Numerically Stabilized Regularized Learning for Intrusion Detection: Conditioning, Scaling, and Cross-Dataset Transfer Analysis
by Miguel Arcos-Argudo, Rodolfo Bojorque and Mauricio Ortiz
Mathematics 2026, 14(15), 2687; https://doi.org/10.3390/math14152687 - 25 Jul 2026
Viewed by 289
Abstract
This paper presents a numerical-computational analysis of ℓ2-regularized logistic learning for binary intrusion detection under heterogeneous datasets, class imbalance, and cross-dataset shift. Rather than proposing a new intrusion detection architecture, the study examines how numerical conditioning, feature scaling, feature set design, [...] Read more.
This paper presents a numerical-computational analysis of ℓ2-regularized logistic learning for binary intrusion detection under heterogeneous datasets, class imbalance, and cross-dataset shift. Rather than proposing a new intrusion detection architecture, the study examines how numerical conditioning, feature scaling, feature set design, threshold selection, false negative behavior, false alarm behavior, and distribution shift affect operational detection performance. Experiments were conducted on CICIDS2017, UNSW-NB15, and CIRA-CIC-DoHBrw-2020 using reproducible train–validation–test protocols over five fixed random seeds. The numerical audit showed that standard scaling reduced the spectral condition number of traffic feature matrices by several orders of magnitude across datasets and feature configurations. However, scaling did not produce uniformly monotonic predictive gains: in some cases, raw feature optimization achieved comparable or higher F1-score, whereas scaled preprocessing produced more controlled false alarm behavior. In-domain experiments showed that dataset-specific features may improve ranking metrics such as area under the receiver-operating-characteristic curve (AUROC) or area under the precision–recall curve (AUPR) without necessarily improving thresholded operational metrics. Cross-dataset transfer experiments revealed strong source–target asymmetry, with transferred thresholds producing either near-zero positive detection or excessive false alarms. Additional robustness experiments with Random Forest and XGBoost improved in-domain F1-score and false negative rate (FNR), but did not eliminate off-domain degradation, with high FNR persisting under direct cross-dataset transfer. Finally, a Kolmogorov–Smirnov-based distribution shift analysis showed that in-domain discrepancies were small, whereas cross-dataset discrepancies were consistently large under common standardized traffic features. These findings suggest that numerical stability, ranking quality, thresholded detection performance, false negative and false alarm behavior, and distribution shift should be analyzed jointly when evaluating intrusion detection models. Full article
(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics: Theory, Methods, and Applications)
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