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Axioms
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Mathematical Models and Simulations, 2nd Edition
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Mathematical Models and Simulations, 2nd Edition

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

Deadline for manuscript submissions: 20 March 2025 | Viewed by 2145

Special Issue Editor

Dr. Giovanni Nastasi

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Catania, Viale Andrea Doria 6, 95125 Catania, Italy
Interests: semiconductor modeling and simulations; kinetic models; numerical solutions of PDEs; Monte Carlo methods; optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is a continuation of our previous Special Issue, entitled "Mathematical Models and Simulations". Mathematical models constitute a fundamental tool for the understanding of physical phenomena, biological systems, and finance and engineering. In addition to theoretical aspects, simulations play a primary role in applications, because they allow for the prediction of the behavior of quantities of interest.

The scope of this Special Issue is to collect papers in the field of mathematical physics, where different categories of mathematical models are presented: deterministic, i.e., based on ordinary or partial differential equations, and stochastic, i.e., defined by stochastic processes or based on stochastic differential equations. It would be beneficial to investigate the mathematical aspects of the presented models. In addition, to provide realistic applications, numerical simulations are encouraged. Several numerical methods suited to the specific problem can be adopted, i.e., finite differences and finite volume schemes, finite elements, and discontinuous Galerkin and Monte Carlo methods. Usually, simulations are performed by adopting real data for the parameters, and the models can also be optimized on datasets if available.

Dr. Giovanni Nastasi
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 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

  • mathematical models
  • ordinary differential equations
  • partial differential equations
  • stochastic processes
  • stochastic differential equations
  • finite difference schemes
  • finite volume schemes
  • finite element method
  • discontinuous galerkin method
  • monte carlo method

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Related Special Issue

Published Papers (3 papers)

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Research

11 pages, 268 KiB  
Article
Hamiltonian Formulation for Continuous Systems with Second-Order Derivatives: A Study of Podolsky Generalized Electrodynamics
by Yazen M. Alawaideh, Alina Alb Lupas, Bashar M. Al-khamiseh, Majeed A. Yousif, Pshtiwan Othman Mohammed and Y. S. Hamed
Axioms 2024, 13(10), 665; https://doi.org/10.3390/axioms13100665 - 26 Sep 2024
Viewed by 353
Abstract
This paper presents an analysis of the Hamiltonian formulation for continuous systems with second-order derivatives derived from Dirac’s theory. This approach offers a unique perspective on the equations of motion compared to the traditional Euler–Lagrange formulation. Focusing on Podolsky’s generalized electrodynamics, the Hamiltonian [...] Read more.
This paper presents an analysis of the Hamiltonian formulation for continuous systems with second-order derivatives derived from Dirac’s theory. This approach offers a unique perspective on the equations of motion compared to the traditional Euler–Lagrange formulation. Focusing on Podolsky’s generalized electrodynamics, the Hamiltonian and corresponding equations of motion are derived. The findings demonstrate that both Hamiltonian and Euler–Lagrange formulations yield equivalent results. This study highlights the Hamiltonian approach as a valuable alternative for understanding the dynamics of second-order systems, validated through a specific application within generalized electrodynamics. The novelty of the research lies in developing advanced theoretical models through Hamiltonian formalism for continuous systems with second-order derivatives. The research employs an alternative method to the Euler–Lagrange formulas by applying Dirac’s theory to study the generalized Podolsky electrodynamics, contributing to a better understanding of complex continuous systems. Full article
(This article belongs to the Special Issue Mathematical Models and Simulations, 2nd Edition)
20 pages, 866 KiB  
Article
Local Influence for the Thin-Plate Spline Generalized Linear Model
by Germán Ibacache-Pulgar, Pablo Pacheco, Orietta Nicolis and Miguel Angel Uribe-Opazo
Axioms 2024, 13(6), 346; https://doi.org/10.3390/axioms13060346 - 23 May 2024
Viewed by 607
Abstract
Thin-Plate Spline Generalized Linear Models (TPS-GLMs) are an extension of Semiparametric Generalized Linear Models (SGLMs), because they allow a smoothing spline to be extended to two or more dimensions. This class of models allows modeling a set of data in which it is [...] Read more.
Thin-Plate Spline Generalized Linear Models (TPS-GLMs) are an extension of Semiparametric Generalized Linear Models (SGLMs), because they allow a smoothing spline to be extended to two or more dimensions. This class of models allows modeling a set of data in which it is desired to incorporate the non-linear joint effects of some covariates to explain the variability of a certain variable of interest. In the spatial context, these models are quite useful, since they allow the effects of locations to be included, both in trend and dispersion, using a smooth surface. In this work, we extend the local influence technique for the TPS-GLM model in order to evaluate the sensitivity of the maximum penalized likelihood estimators against small perturbations in the model and data. We fit our model through a joint iterative process based on Fisher Scoring and weighted backfitting algorithms. In addition, we obtained the normal curvature for the case-weight perturbation and response variable additive perturbation schemes, in order to detect influential observations on the model fit. Finally, two data sets from different areas (agronomy and environment) were used to illustrate the methodology proposed here. Full article
(This article belongs to the Special Issue Mathematical Models and Simulations, 2nd Edition)
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15 pages, 331 KiB  
Article
On a Stability of Non-Stationary Discrete Schemes with Respect to Interpolation Errors
by Raimondas Čiegis, Olga Suboč and Remigijus Čiegis
Axioms 2024, 13(4), 244; https://doi.org/10.3390/axioms13040244 - 9 Apr 2024
Viewed by 775
Abstract
The aim of this article is to analyze the efficiency and accuracy of finite-difference and finite-element Galerkin schemes for non-stationary hyperbolic and parabolic problems. The main problem solved in this article deals with the construction of accurate and efficient discrete schemes on nonuniform [...] Read more.
The aim of this article is to analyze the efficiency and accuracy of finite-difference and finite-element Galerkin schemes for non-stationary hyperbolic and parabolic problems. The main problem solved in this article deals with the construction of accurate and efficient discrete schemes on nonuniform and dynamic grids in time and space. The presented stability and convergence analysis enables improving the existing accuracy estimates. The obtained stability results show explicitly the rate of accumulation of interpolation and projection errors that arise due to the movement of grid points. It is shown that the cases when the time grid steps are doubled or halved have different stability properties. As an additional technique to improve the accuracy of discretizations on non-stationary space grids, it is recommended to use projection operators instead of interpolation operators. This technique is used to solve a test parabolic problem. The results of specially selected computational experiments are also presented, and they confirm the accuracy of all theoretical error estimates obtained in this article. Full article
(This article belongs to the Special Issue Mathematical Models and Simulations, 2nd Edition)
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