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Mathematics
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Mathematical Modeling, Numerical Analysis and Scientific Computing, with Their Applications
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Mathematical Modeling, Numerical Analysis and Scientific Computing, with Their Applications

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

Deadline for manuscript submissions: closed (20 January 2024) | Viewed by 9258

Special Issue Editor

Dr. Songting Luo

E-Mail Website
Guest Editor
Department of Mathematics, Iowa State University, Ames, IA 50011, USA
Interests: mathematical modeling; numerical analysis; scientific computing; partial differential equations

Special Issue Information

Dear Colleagues,

Mathematical modeling, numerical analysis and scientific computing have been playing a significant role in solving real-world problems, with applications arising from various areas in science, engineering, and technology.

This Special Issue will present recent research results in mathematical modeling, numerical analysis, scientific computing, and their applications. Papers on the development and analysis of novel methods and models in all areas of mathematical modeling, numerical analysis and scientific computing are welcome. More specifically, papers on but not limited to the following broad topics are welcome:

  • Mathematical modeling and simulation of applications in science, engineering, and
  • Numerical analysis of ODEs, PDEs, and
  • Scientific computing and algorithms for applications in science, engineering, and technology.

Dr. Songting Luo
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

  • mathematical modeling and simulation
  • numerical analysis
  • scientific computing
  • computational methods and algorithms
  • computational, applied and industrial mathematics
  • applications in science, engineering and technology

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (4 papers)

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Research

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28 pages, 8052 KiB  
Article
Spherical Gravity Forwarding of Global Discrete Grid Cells by Isoparametric Transformation
by Shujin Cao, Peng Chen, Guangyin Lu, Yihuai Deng, Dongxin Zhang and Xinyue Chen
Mathematics 2024, 12(6), 885; https://doi.org/10.3390/math12060885 - 17 Mar 2024
Cited by 1 | Viewed by 975
Abstract
For regional or even global geophysical problems, the curvature of the geophysical model cannot be approximated as a plane, and its curvature must be considered. Tesseroids can fit the curvature, but their shapes vary from almost rectangular at the equator to almost triangular [...] Read more.
For regional or even global geophysical problems, the curvature of the geophysical model cannot be approximated as a plane, and its curvature must be considered. Tesseroids can fit the curvature, but their shapes vary from almost rectangular at the equator to almost triangular at the poles, i.e., degradation phenomena. Unlike other spherical discrete grids (e.g., square, triangular, and rhombic grids) that can fit the curvature, the Discrete Global Grid System (DGGS) grid can not only fit the curvature but also effectively avoid degradation phenomena at the poles. In addition, since it has only edge-adjacent grids, DGGS grids have consistent adjacency and excellent angular resolution. Hence, DGGS grids are the best choice for discretizing the sphere into cells with an approximate shape and continuous scale. Compared with the tesseroid, which has no analytical solution but has a well-defined integral limit, the DGGS cell (prisms obtained from DGGS grids) has neither an analytical solution nor a fixed integral limit. Therefore, based on the isoparametric transformation, the non-regular DGGS cell in the system coordinate system is transformed into the regular hexagonal prism in the local coordinate system, and the DGGS-based forwarding algorithm of the gravitational field is realized in the spherical coordinate system. Different coordinate systems have differences in the integral kernels of gravity fields. In the current literature, the forward modeling research of polyhedrons (the DGGS cell, which is a polyhedral cell) is mostly concentrated in the Cartesian coordinate system. Therefore, the reliability of the DGGS-based forwarding algorithm is verified using the tetrahedron-based forwarding algorithm and the tesseroid-based forwarding algorithm with tiny tesseroids. From the numerical results, it can be concluded that if the distance from observations to sources is too small, the corresponding gravity field forwarding results may also have ambiguous values. Therefore, the minimum distance is not recommended for practical applications. Full article
(This article belongs to the Special Issue Mathematical Modeling, Numerical Analysis and Scientific Computing, with Their Applications)
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13 pages, 670 KiB  
Article
An Efficient Limited Memory Multi-Step Quasi-Newton Method
by Issam A. R. Moghrabi and Basim A. Hassan
Mathematics 2024, 12(5), 768; https://doi.org/10.3390/math12050768 - 4 Mar 2024
Viewed by 992
Abstract
This paper is dedicated to the development of a novel class of quasi-Newton techniques tailored to address computational challenges posed by memory constraints. Such methodologies are commonly referred to as “limited” memory methods. The method proposed herein showcases adaptability by introducing a customizable [...] Read more.
This paper is dedicated to the development of a novel class of quasi-Newton techniques tailored to address computational challenges posed by memory constraints. Such methodologies are commonly referred to as “limited” memory methods. The method proposed herein showcases adaptability by introducing a customizable memory parameter governing the retention of historical data in constructing the Hessian estimate matrix at each iterative stage. The search directions generated through this novel approach are derived from a modified version closely resembling the full memory multi-step BFGS update, incorporating limited memory computation for a singular term to approximate matrix–vector multiplication. Results from numerical experiments, exploring various parameter configurations, substantiate the enhanced efficiency of the proposed algorithm within the realm of limited memory quasi-Newton methodologies category. Full article
(This article belongs to the Special Issue Mathematical Modeling, Numerical Analysis and Scientific Computing, with Their Applications)
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16 pages, 2525 KiB  
Article
Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level
by Arjun Hasibuan, Asep Kuswandi Supriatna, Endang Rusyaman and Md. Haider Ali Biswas
Mathematics 2023, 11(18), 4015; https://doi.org/10.3390/math11184015 - 21 Sep 2023
Cited by 2 | Viewed by 1815
Abstract
In this work, we examine a predator–prey model that considers the implicit marine reserve in prey species and a linear function of critical biomass level. The model’s basic properties (existence, uniqueness, positivity, boundedness, and permanence) and equilibrium points are determined. We obtain three [...] Read more.
In this work, we examine a predator–prey model that considers the implicit marine reserve in prey species and a linear function of critical biomass level. The model’s basic properties (existence, uniqueness, positivity, boundedness, and permanence) and equilibrium points are determined. We obtain three equilibrium points: the trivial equilibrium point, the equilibrium point where there is no harvest, and the co-existing equilibrium point. The local and global stability of each equilibrium point of the model is explored. Moreover, the interior equilibrium point is always globally asymptotically stable, and the system experiences no limit cycles around the interior equilibrium point. Numerical simulations are conducted to illustrate the theoretical results obtained. Finally, we find overlapping conditions regarding the dynamics between the model we developed and a model that considers a constant critical biomass level for certain parameters. Full article
(This article belongs to the Special Issue Mathematical Modeling, Numerical Analysis and Scientific Computing, with Their Applications)
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Review

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36 pages, 4184 KiB  
Review
Harmonics Signal Feature Extraction Techniques: A Review
by Minh Ly Duc, Petr Bilik and Radek Martinek
Mathematics 2023, 11(8), 1877; https://doi.org/10.3390/math11081877 - 15 Apr 2023
Cited by 6 | Viewed by 4709
Abstract
Harmonic estimation is essential for mitigating or suppressing harmonic distortions in power systems. The most important idea is that spectrum analysis, waveform estimation, harmonic source classification, source location, the determination of harmonic source contributions, data clustering, and filter-based harmonic elimination capacity are also [...] Read more.
Harmonic estimation is essential for mitigating or suppressing harmonic distortions in power systems. The most important idea is that spectrum analysis, waveform estimation, harmonic source classification, source location, the determination of harmonic source contributions, data clustering, and filter-based harmonic elimination capacity are also considered. The feature extraction method is a fundamental component of the optimization that improves the effectiveness of the Harmonic Mitigation method. In this study, techniques to extract fundamental frequencies and harmonics in the frequency domain, the time domain, and the spatial domain include 67 literature reviews and an overall assessment. The combinations of signal processing with artificial intelligence (AI) techniques are also reviewed and evaluated in this study. The benefit of the feature extraction methods is that the analysis extracts the powerful basic information of the feedback signals from the sensors with the most redundancy, ensuring the highest efficiency for the next sampling process of algorithms. This study provides an overview of the fundamental frequency and harmonic extraction methods of recent years, an analysis, and a presentation of their advantages and limitations. Full article
(This article belongs to the Special Issue Mathematical Modeling, Numerical Analysis and Scientific Computing, with Their Applications)
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