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Axioms
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Advances in Numerical Analysis and Scientific Computing
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Advances in Numerical Analysis and Scientific Computing

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

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 3097

Special Issue Editor

Dr. Qingguo Hong

E-Mail Website
Guest Editor
Department of Mathematics, Pennsylvania State University, University Park, PA, USA
Interests: computational mathematics; numerical analysis; iterative method; applied mathematics

Special Issue Information

Dear Colleagues,

In the last several years, the role of numerical analysis and scientific computing has been dramatically increased, especially for the solution of real-world problems, and for the creation of digital twins of complex real-world objects.

This Special Issue will present recent research results in numerical analysis and scientific computing.

Papers on the production, analysis, and computational performance of new and original methods in all areas of numerical analysis and scientific computing are welcome. More specifically, we welcome papers on topics including but not limited to the following:

  • Scientific computing and algorithms in applications in the sciences (computational physics, computational chemistry, computational bioinformatics, computational engineering, etc.);
  • Mathematical modeling (including, but not limited to, mathematical modeling of engineering and environmental manufacturing processes, industrial systems, heat transfer, fluid mechanics, CFD, and transport phenomena);
  • Numerical problems in dynamical systems, numerical analysis of ODEs, PDEs, and systems;
  • Mathematical methods with application in many artificial intelligence implementations;
  • Neural networks in numerical analysis and scientific computing.

Dr. Qingguo Hong
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

  • computational methods
  • numerical analysis
  • applied and industrial mathematics
  • scientific computing
  • computational methods and algorithms
  • finite element method
  • multigrid methods

Published Papers (2 papers)

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Research

18 pages, 18693 KiB  
Article
A Study of The Stochastic Burgers’ Equation Using The Dynamical Orthogonal Method
by Mohamed El-Beltagy, Ragab Mahdi and Adeeb Noor
Axioms 2023, 12(2), 152; https://doi.org/10.3390/axioms12020152 - 01 Feb 2023
Viewed by 1111
Abstract
In the current work, the stochastic Burgers’ equation is studied using the Dynamically Orthogonal (DO) method. The DO presents a low-dimensional representation for the stochastic fields. Unlike many other methods, it has a time-dependent property on both the spatial basis and stochastic coefficients, [...] Read more.
In the current work, the stochastic Burgers’ equation is studied using the Dynamically Orthogonal (DO) method. The DO presents a low-dimensional representation for the stochastic fields. Unlike many other methods, it has a time-dependent property on both the spatial basis and stochastic coefficients, with flexible representation especially in the strongly transient and nonstationary problems. We consider a computational study and application of the DO method and compare it with the Polynomial Chaos (PC) method. For comparison, both the stochastic viscous and inviscid Burgers’ equations are considered. A hybrid approach, combining the DO and PC is proposed in case of deterministic initial conditions to overcome the singularities that occur in the DO method. The results are verified with the stochastic collocation method. Overall, we observe that the DO method has a higher rate of convergence as the number of modes increases. The DO method is found to be more efficient than PC for the same level of accuracy, especially for the case of high-dimensional parametric spaces. The inviscid Burgers’ equation is analyzed to study the shock wave formation when using the DO after suitable handling of the convective term. The results show that the sinusoidal wave shape is distorted and sharpened as the time evolves till the shock wave occurs. Full article
(This article belongs to the Special Issue Advances in Numerical Analysis and Scientific Computing)
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25 pages, 2512 KiB  
Article
Study on Comprehensive Evaluation Based on AHP-MADM Model for Patent Value of Balanced Vehicle
by Zhili Huang, Jinli Li and Hongge Yue
Axioms 2022, 11(9), 481; https://doi.org/10.3390/axioms11090481 - 18 Sep 2022
Cited by 6 | Viewed by 1515
Abstract
With the development of science and technology, people’s travel modes have become more diversified, and self-balancing vehicles have become a popular travel tool for young people. However, in recent years, due to its quality instability, many regions have issued relevant bans, affecting the [...] Read more.
With the development of science and technology, people’s travel modes have become more diversified, and self-balancing vehicles have become a popular travel tool for young people. However, in recent years, due to its quality instability, many regions have issued relevant bans, affecting the development of the balanced vehicle industry. In order to better understand balancing vehicle technology, this paper starts with the balancing vehicle patent, and carries out the following research: This paper first introduces the background and current situation of balanced vehicles and the patent. Then, the principle and model of multi-attribute decision-making based on the analytic hierarchy process (AHP-MADM) are described. According to the three-dimensional patent valuation system issued by the State Intellectual Property Office, a core patent valuation system is established. Then, the weights of patent evaluation attributes are calculated by the improved AHP. After, the patent value of the self-balancing vehicle is evaluated using the established AHP-MADM model. On this basis, the status of patent research and the development of self-balancing vehicles is studied to provide a reference for relevant industry personnel, especially R & D personnel, in future product technology updates and patent layout. Full article
(This article belongs to the Special Issue Advances in Numerical Analysis and Scientific Computing)
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