Mathematical Models and Simulations II

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

Deadline for manuscript submissions: 20 August 2024 | Viewed by 499

Special Issue Editor


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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
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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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Published Papers (1 paper)

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Research

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 - 09 Apr 2024
Viewed by 358
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 II)
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