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Axioms
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Computational Mathematics in Engineering and Applied Science
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Computational Mathematics in Engineering and Applied Science

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

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 6721

Special Issue Editors

Dr. Weifeng Pan

E-Mail Website
Guest Editor
School of Computer Science and Information Engineering, Zhejiang Gongshang University, Hangzhou 310018, China
Interests: intelligent computing; complex networks; software engineering; service computing
Dr. Hua Ming

E-Mail Website
Guest Editor
School of Engineering and Computer Science, Oakland University, Rochester, MI 48309, USA
Interests: situation-aware software services; complex networks; software verification; big-data-oriented software-intensive systems; domain-specific programming language design and implementation
Prof. Dr. Dae-Kyoo Kim

E-Mail Website
Guest Editor
School of Engineering and Computer Science, Oakland University, Rochester, MI 48309, USA
Interests: software design patterns; software access control; software modeling; software security and interoperability in smart grid; software maintenance; software architecture; software process; requirements engineering; software verification and validation; self-adaptive systems; mobile software; automotive software; Distributed Data Service (DDS)

Special Issue Information

Dear Colleagues,

Computational mathematics has been the foundation of modern scientific computing. It mainly focuses on developing and analyzing numerical algorithms. Generally, numerical algorithms and numerical analysis involve four types of algorithms, i.e., numerical linear algebra, numerical optimization, numerical solution of differential equations, and stochastic data modeling. We can find a wide range of applications of these numerical algorithms in engineering and applied science, and their power and efficiency have been widely demonstrated. During the last decade, in computational mathematics, a large number of efficient numerical algorithms have been proposed, covering many different topics, such as deep learning, evolutionary computation, and swarm intelligence. The objective of this Special Issue is to provide a comprehensive collection of research work on the theoretical and practical aspects of computational mathematics, especially those that provide vanguard solutions to challenging problems or can demonstrate competitive performance in engineering and applied science. Original research articles presenting novel in-depth fundamental research are welcomed, along with review articles discussing the current state of the art.

Dr. Weifeng Pan
Dr. Hua Ming
Prof. Dr. Dae-Kyoo Kim
Guest Editors

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

  • numerical linear algebra
  • numerical optimization
  • numerical solution of differential equations
  • stochastic data modeling
  • deep learning
  • clustering methods
  • artificial neural networks
  • simulated annealing
  • evolutionary computation: genetic algorithms, genetic programming, etc.
  • swarm intelligence: Ant/Bee/Bat/firefly algorithms, particle swarm optimization, etc.
  • combinatorial, discrete, binary, constrained, multi-objective, multi-modal, dynamic, and large-scale optimization
  • memetic computing
  • autonomic computing
  • analysis of numerical algorithms
  • any novel competitive application in software engineering, network science, service computing, and the IoT
  • any novel competitive application with potential impact on engineering and applied science

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Published Papers (4 papers)

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Research

25 pages, 9318 KiB  
Article
Research on the Calculation Model and Control Method of Initial Supporting Force for Temporary Support in the Underground Excavation Roadway of Coal Mine
by Dongjie Wang, Rui Li, Jiameng Cheng, Weixiong Zheng, Yang Shen, Sihai Zhao and Miao Wu
Axioms 2023, 12(10), 948; https://doi.org/10.3390/axioms12100948 - 5 Oct 2023
Cited by 3 | Viewed by 1556
Abstract
This paper proposes a temporary support system for improving the efficiency and safety of underground roadway excavation in coal mines. Firstly, this study establishes a calculation model for the initial supporting force of the excavation of roadway temporary support and a gray system-based [...] Read more.
This paper proposes a temporary support system for improving the efficiency and safety of underground roadway excavation in coal mines. Firstly, this study establishes a calculation model for the initial supporting force of the excavation of roadway temporary support and a gray system-based automatic prediction model for the initial supporting force level, based on the mechanism of temporary support controlling the roof. These models enable the prediction of the required initial supporting force at different locations along the roadway’s temporary support area, thereby providing a basis for controlling the initial supporting force of the temporary support system. To achieve efficient and adaptive control of the initial supporting force of temporary supports at different locations, this study designs a support force controller based on Simulated Annealing Particle Swarm Optimization Proportional-Integral-Derivative (SAPSO-PID). This study establishes a mathematical model for the hydraulic cylinder pressure system controlled by the temporary support overflow valve and conducts a stability analysis and model verification. The study constructs a simulation control system for the initial supporting force based on SAPSO-PID using the combined simulation platform of AMESim and Matlab. The simulation results demonstrate that the proposed support force control system efficiently achieves adaptive control of the initial supporting force of temporary supports. An experimental system in the underground roadway of a coal mine is constructed to validate the results of the simulation analysis. Full article
(This article belongs to the Special Issue Computational Mathematics in Engineering and Applied Science)
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13 pages, 332 KiB  
Article
A Two-Step Newton Algorithm for the Weighted Complementarity Problem with Local Biquadratic Convergence
by Xiangjing Liu, Yihan Liu and Jianke Zhang
Axioms 2023, 12(9), 897; https://doi.org/10.3390/axioms12090897 - 20 Sep 2023
Cited by 1 | Viewed by 1085
Abstract
We discuss the weighted complementarity problem, extending the nonlinear complementarity problem on Rn. In contrast to the NCP, many equilibrium problems in science, engineering, and economics can be transformed into WCPs for more efficient methods. Smoothing Newton algorithms, known for their [...] Read more.
We discuss the weighted complementarity problem, extending the nonlinear complementarity problem on Rn. In contrast to the NCP, many equilibrium problems in science, engineering, and economics can be transformed into WCPs for more efficient methods. Smoothing Newton algorithms, known for their at least locally superlinear convergence properties, have been widely applied to solve WCPs. We suggest a two-step Newton approach with a local biquadratic order convergence rate to solve the WCP. The new method needs to calculate two Newton equations at each iteration. We also insert a new term, which is of crucial importance for the local biquadratic convergence properties when solving the Newton equation. We demonstrate that the solution to the WCP is the accumulation point of the iterative sequence produced by the approach. We further demonstrate that the algorithm possesses local biquadratic convergence properties. Numerical results indicate the method to be practical and efficient. Full article
(This article belongs to the Special Issue Computational Mathematics in Engineering and Applied Science)
15 pages, 1327 KiB  
Article
Strong Convergence of a Two-Step Modified Newton Method for Weighted Complementarity Problems
by Xiangjing Liu and Jianke Zhang
Axioms 2023, 12(8), 742; https://doi.org/10.3390/axioms12080742 - 28 Jul 2023
Cited by 1 | Viewed by 981
Abstract
This paper focuses on the weighted complementarity problem (WCP), which is widely used in the fields of economics, sciences and engineering. Not least because of its local superlinear convergence rate, smoothing Newton methods have widespread application in solving various optimization problems. A two-step [...] Read more.
This paper focuses on the weighted complementarity problem (WCP), which is widely used in the fields of economics, sciences and engineering. Not least because of its local superlinear convergence rate, smoothing Newton methods have widespread application in solving various optimization problems. A two-step smoothing Newton method with strong convergence is proposed. With a smoothing complementary function, the WCP is reformulated as a smoothing set of equations and solved by the proposed two-step smoothing Newton method. In each iteration, the new method computes the Newton equation twice, but using the same Jacobian, which can avoid consuming a lot of time in the calculation. To ensure the global convergence, a derivative-free line search rule is inserted. At the same time, we develop a different term in the solution of the smoothing Newton equation, which guarantees the local strong convergence. Under appropriate conditions, the algorithm has at least quadratic or even cubic local convergence. Numerical experiments indicate the stability and effectiveness of the new method. Moreover, compared to the general smoothing Newton method, the two-step smoothing Newton method can significantly improve the computational efficiency without increasing the computational cost. Full article
(This article belongs to the Special Issue Computational Mathematics in Engineering and Applied Science)
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19 pages, 5367 KiB  
Article
A Reliable Computational Scheme for Stochastic Reaction–Diffusion Nonlinear Chemical Model
by Muhammad Shoaib Arif, Kamaleldin Abodayeh and Yasir Nawaz
Axioms 2023, 12(5), 460; https://doi.org/10.3390/axioms12050460 - 9 May 2023
Cited by 9 | Viewed by 1697
Abstract
The main aim of this contribution is to construct a numerical scheme for solving stochastic time-dependent partial differential equations (PDEs). This has the advantage of solving problems with positive solutions. The scheme provides conditions for obtaining positive solutions, which the existing Euler–Maruyama method [...] Read more.
The main aim of this contribution is to construct a numerical scheme for solving stochastic time-dependent partial differential equations (PDEs). This has the advantage of solving problems with positive solutions. The scheme provides conditions for obtaining positive solutions, which the existing Euler–Maruyama method cannot do. In addition, it is more accurate than the existing stochastic non-standard finite difference (NSFD) method. Theoretically, the suggested scheme is more accurate than the current NSFD method, and its stability and consistency analysis are also shown. The scheme is applied to the linear scalar stochastic time-dependent parabolic equation and the nonlinear auto-catalytic Brusselator model. The deficiency of the NSFD in terms of accuracy is also shown by providing different graphs. Many observable occurrences in the physical world can be traced back to certain chemical concentrations. Examining and understanding the inter-diffusion between chemical concentrations is important, especially when they coincide. The Brusselator model is the gold standard for describing the relationship between chemical concentrations and other variables in chemical systems. A computational code for the proposed model scheme may be made available to readers upon request for convenience. Full article
(This article belongs to the Special Issue Computational Mathematics in Engineering and Applied Science)
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