Numerical Analysis and Its Application and Symmetry

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 October 2022) | Viewed by 3432

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
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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
Department of Civil Engineering, Polytechnic School, Democritus University of Thrace, Kimmeria Campus, 671 00 Xanthi, Greece
Interests: applied mathematics; numerical analysis; numerical solution of differential equations
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Special Issue Information

Dear Colleagues,

I would like to inform you that the Special Issue “Numerical Analysis and Its Applications and Symmetry” welcomes papers, with research including the study, design, development, analysis, and/or programming of numerical schemes in order to apply them to distinguished problems or families of problems.

Numerical analysis is a major branch of Mathematics which consists of mathematical approximation techniques and computational methods. Applications of numerical methods can be found in a wide range of problems in engineering, physical sciences, life and medical sciences, economic sciences, psychology, etc., and in general to problems, where classical analytical methods cannot provide a solution.

Symmetry is a fundamental concept in science. It is a property, which is preserved through a mathematical operation or a transformation of an object onto itself. Symmetry can be found in all aspects of science. It is also a property of a wide range of numerical methods.

The Special Issue focuses in numerical approaches and solutions of ordinary differential equations(ODEs), partial differential equations(PDEs), stochastic differential equations(SDEs), delay differential equations(DDEs), differential-algebraic equations(DAEs). We are also interested in numerical methods for the solution of nonlinear equations or systems of nonlinear equations. Furthermore, we are seeking novel research in the field of numerical analysis related to linear algebra, optimization, control theory, fluid dynamics, thermodynamics, quantum dynamics and applications of the above to problems in theoretical sciences and engineering and also with connection to symmetry.

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

Keywords

  • Numerical methods
  • Differential equations and Differential-algebraic equations
  • Systems of linear and non-linear equations
  • Optimization
  • Control theory
  • Fluid dynamics
  • Thermodynamics
  • Quantum dynamics

Published Papers (2 papers)

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Research

20 pages, 385 KiB  
Article
Cross-Gramian-Based Model Reduction for Descriptor Systems
by Yiqin Lin
Symmetry 2022, 14(11), 2400; https://doi.org/10.3390/sym14112400 - 13 Nov 2022
Cited by 1 | Viewed by 943
Abstract
In this paper, we explore model order reduction for large-scale square descriptor systems. A balancing-free square-root method is proposed. The balancing-free square-root method is based on two cross Gramians, one of which is known as the proper cross Gramian and the other as [...] Read more.
In this paper, we explore model order reduction for large-scale square descriptor systems. A balancing-free square-root method is proposed. The balancing-free square-root method is based on two cross Gramians, one of which is known as the proper cross Gramian and the other as the improper cross Gramian. The proper cross Gramian is the unique solution of a projected generalized continuous-time Sylvester equation, and the improper cross Gramian solves a projected generalized discrete-time Sylvester equation. In order to compute the low-rank factors of these two cross Gramians, we extend the low-rank iteration of the alternating direction implicit method and the Smith method to the projected generalized Sylvester equations. We illustrate the effectiveness of the balance truncation method with one numerical example. Full article
(This article belongs to the Special Issue Numerical Analysis and Its Application and Symmetry)
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10 pages, 1220 KiB  
Article
Numerical Investigation of the Two-Dimensional Fredholm Integral Equations of the Second Kind by Bernstein Operators
by Ovgu Cidar Iyikal
Symmetry 2022, 14(3), 625; https://doi.org/10.3390/sym14030625 - 21 Mar 2022
Viewed by 1350
Abstract
In this study, the numerical solutions of linear two-dimensional Fredholm integral equations of the second kind via Bernstein operators are considered. The method is presented with illustrative examples for regularized-equal and Chebyshev collocation points. The obtained numerical results from illustrative examples show that [...] Read more.
In this study, the numerical solutions of linear two-dimensional Fredholm integral equations of the second kind via Bernstein operators are considered. The method is presented with illustrative examples for regularized-equal and Chebyshev collocation points. The obtained numerical results from illustrative examples show that the proposed numerical algorithm is accurate and efficient for solving linear two-dimensional Fredholm integral equation of the second kind. Full article
(This article belongs to the Special Issue Numerical Analysis and Its Application and Symmetry)
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