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Mathematics
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Computational Mathematics: Advanced Methods and Applications
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Computational Mathematics: Advanced Methods and Applications

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

Deadline for manuscript submissions: 20 March 2025 | Viewed by 942

Special Issue Editor

Dr. Nebojša Dedović

E-Mail Website
Guest Editor
Department for Agricultural Engineering, Faculty of Agriculture, University of Novi Sad, 21000 Novi Sad, Serbia
Interests: mathematical analysis; statistics; partial differential equations; mathematical modelling; numerical mathematics

Special Issue Information

Dear Colleagues,

We are pleased to invite you to submit your contributions to this Special Issue titled ‘Computational Mathematics: Advanced Methods and Applications’. We aim to make your manuscripts accessible to a broad scientific audience who are interested in the application of methods such as partial differential equations and difference equations in various fields, including mathematics, sciences, etc. The covered topics may include models of conservation laws, numerical approximations in Mathematica or MATLAB, optimization using the response surface method, and matrix calculus applied on best linear unbiased prediction.

Dr. Nebojša Dedović
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. 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

  • classical partial/differential/difference equations
  • conservation laws
  • shock and rarefaction waves
  • application of mathematics in Science
  • response surface method
  • Mathematica/MATLAB
  • statistics
  • best linear unbiased prediction

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Published Papers (1 paper)

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Research

19 pages, 852 KiB  
Article
Approximation of the Interactions of Rarefaction Waves by the Wave Front Tracking Method
by Nebojša Dedović
Mathematics 2024, 12(13), 2099; https://doi.org/10.3390/math12132099 - 4 Jul 2024
Viewed by 574
Abstract
The interaction of two simple delta shock waves for a pressureless gas dynamic system is considered. The result of the interaction is a delta shock wave with constant speed. This interaction is approximated by letting the perturbed parameter in the Euler equations for [...] Read more.
The interaction of two simple delta shock waves for a pressureless gas dynamic system is considered. The result of the interaction is a delta shock wave with constant speed. This interaction is approximated by letting the perturbed parameter in the Euler equations for isentropic fluids go to zero. Each delta shock wave is approximated by two shock waves of the first and second family when the perturbed parameter goes to zero. These shock waves are solutions of two Riemann problems at time t=0. The solution of the Riemann problem for t>0 can also contain rarefaction waves. If the perturbed parameter approaches 0, the strength of the rarefaction waves increases and the number of interactions of the rarefaction waves increases, as well. When two split rarefaction waves interact, the number of Riemann problems to be solved is m1·m2, where mi is the number of ith rarefaction waves. The main topic of this paper is to develop an algorithm that reduces the number of these Riemann problems. The algorithm is based on the determination of the intermediate states that make the Rankine–Hugoniot deficit small. The approximated wave front tracking algorithm was used for the numerical verification of these interactions. The theoretical background was the concept of the shadow wave solution. Full article
(This article belongs to the Special Issue Computational Mathematics: Advanced Methods and Applications)
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