Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.0
2.3
Journals
Mathematics
Special Issues
Numerical Analysis in Computational Mathematics
share announcement

Numerical Analysis in Computational Mathematics

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

Deadline for manuscript submissions: 31 July 2025 | Viewed by 7590

Special Issue Editors

Dr. Thái Anh Nhan

E-Mail Website
Guest Editor
Mathematics, Menlo College, Atherton, CA 94027, USA
Interests: numerical analysis; applied math; scientific computing
Prof. Dr. Istvan Farago

E-Mail Website
Guest Editor
Department of Applied Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
Interests: numerical analysis; differential equations; mathematical modeling of real-life problems; epidemic propagation

Special Issue Information

Dear Colleagues,

The Special Issue on Numerical Analysis in Computational Methods provides a high-quality venue for recent advances in the design and development of numerical and computational algorithms for all aspects in Applied Mathematics. We invite researchers to contribute high-quality original research articles as well as review articles on recent advances including, but not limited to, theoretical and applied numerical algorithms, analysis, and methods, applied and computational methods, scientific computing, computer simulations, optimization techniques, and advances in other branches of applied science with a computational mathematics component.

Dr. Thái Anh Nhan
Prof. Dr. Istvan Farago
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. 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

  • numerical algorithms, analysis, and methods
  • applications of numerical algorithms, analysis, and methods
  • applied and computational mathematics
  • scientific computing
  • computer simulations
  • optimization techniques

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

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

Published Papers (6 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

28 pages, 18090 KiB  
Article
AFSA-FastICA-CEEMD Rolling Bearing Fault Diagnosis Method Based on Acoustic Signals
by Jin Yan, Fubing Zhou, Xu Zhu and Dapeng Zhang
Mathematics 2025, 13(5), 884; https://doi.org/10.3390/math13050884 - 6 Mar 2025
Viewed by 397
Abstract
As one of the key components in rotating machinery, rolling bearings have a crucial impact on the safety and efficiency of production. Acoustic signal is a commonly used method in the field of mechanical fault diagnosis, but an overlapping phenomenon occurs very easily, [...] Read more.
As one of the key components in rotating machinery, rolling bearings have a crucial impact on the safety and efficiency of production. Acoustic signal is a commonly used method in the field of mechanical fault diagnosis, but an overlapping phenomenon occurs very easily, which affects the diagnostic accuracy. Therefore, effective blind source separation and noise reduction of the acoustic signals generated between different devices is the key to bearing fault diagnosis using acoustic signals. To this end, this paper proposes a blind source separation method based on an AFSA-FastICA (Artificial Fish Swarm Algorithm, AFSA). Firstly, the foraging and clustering characteristics of the AFSA algorithm are utilized to perform global optimization on the aliasing matrix W, and then inverse transformation is performed on the global optimal solution W, to obtain a preliminary estimate of the source signal. Secondly, the estimated source signal is subjected to CEEMD noise reduction, and after obtaining the modal components of each order, the number of interrelationships is used as a constraint on the modal components, and signal reconstruction is performed. Finally, the signal is subjected to frequency domain feature extraction and bearing fault diagnosis. The experimental results indicate that, the new method successfully captures three fault characteristic frequencies (1fi, 2fi, and 3fi), with their energy distribution concentrated in the range of 78.9 Hz to 228.7 Hz, indicative of inner race faults. Similarly, when comparing the different results with each other, the denoised source signal spectrum successfully captures the frequencies 1fo, 2fo, and 3fo and their sideband components, which are characteristic of outer race faults. The sideband components generated in the above spectra are preliminarily judged to be caused by impacts between the fault location and nearby components, resulting in modulated frequency bands where the modulation frequency corresponds to the rotational frequency and its harmonics. Experiments show that the method can effectively diagnose the bearing faults. Full article
(This article belongs to the Special Issue Numerical Analysis in Computational Mathematics)
►▼ Show Figures

Figure 1

10 pages, 725 KiB  
Article
Coarse-Gridded Simulation of the Nonlinear Schrödinger Equation with Machine Learning
by Benjamin F. Akers and Kristina O. F. Williams
Mathematics 2024, 12(17), 2784; https://doi.org/10.3390/math12172784 - 9 Sep 2024
Cited by 1 | Viewed by 851
Abstract
A numerical method for evolving the nonlinear Schrödinger equation on a coarse spatial grid is developed. This trains a neural network to generate the optimal stencil weights to discretize the second derivative of solutions to the nonlinear Schrödinger equation. The neural network is [...] Read more.
A numerical method for evolving the nonlinear Schrödinger equation on a coarse spatial grid is developed. This trains a neural network to generate the optimal stencil weights to discretize the second derivative of solutions to the nonlinear Schrödinger equation. The neural network is embedded in a symmetric matrix to control the scheme’s eigenvalues, ensuring stability. The machine-learned method can outperform both its parent finite difference method and a Fourier spectral method. The trained scheme has the same asymptotic operation cost as its parent finite difference method after training. Unlike traditional methods, the performance depends on how close the initial data are to the training set. Full article
(This article belongs to the Special Issue Numerical Analysis in Computational Mathematics)
►▼ Show Figures

Figure 1

14 pages, 397 KiB  
Article
Fractional Modelling of H2O2-Assisted Oxidation by Spanish broom peroxidase
by Vinh Quang Mai and Thái Anh Nhan
Mathematics 2024, 12(9), 1411; https://doi.org/10.3390/math12091411 - 5 May 2024
Viewed by 1110
Abstract
The H2O2-assisted oxidation by a peroxidase enzyme takes place to help plants maintain the concentrations of organic compounds at physiological levels. Cells regulate the oxidation rate by inhibiting the action of this enzyme. The cells use two inhibitory processes [...] Read more.
The H2O2-assisted oxidation by a peroxidase enzyme takes place to help plants maintain the concentrations of organic compounds at physiological levels. Cells regulate the oxidation rate by inhibiting the action of this enzyme. The cells use two inhibitory processes to regulate the enzyme: a noncompetitive substrate inhibitory process and a competitive substrate inhibitory process. Numerous applications of peroxidase have been developed in clinical biochemistry, enzyme immunoassays, the treatment of waste water containing phenolic compounds, the synthesis of various aromatic chemicals, and the removal of peroxide from industrial wastes. The kinetic mechanism of the Spanish broom peroxidase enzyme is a Ping Pong Bi Bi mechanism with the presence of competitive inhibition by substrates. A mathematical model may help in identifying the key mechanism from amongst a set of competing mechanisms. In this study, we developed a fractional mathematical model to describe the H2O2-supported oxidation by the enzyme Spanish broom peroxidase. Numerical simulations of the model produced results that are consistent with the known behaviour of Spanish broom peroxidase. Finally, some future investigations of the study are briefly indicated as well. Full article
(This article belongs to the Special Issue Numerical Analysis in Computational Mathematics)
►▼ Show Figures

Figure 1

19 pages, 5521 KiB  
Article
Deep Neural Networks with Spacetime RBF for Solving Forward and Inverse Problems in the Diffusion Process
by Cheng-Yu Ku, Chih-Yu Liu, Yu-Jia Chiu and Wei-Da Chen
Mathematics 2024, 12(9), 1407; https://doi.org/10.3390/math12091407 - 4 May 2024
Cited by 2 | Viewed by 1662
Abstract
This study introduces a deep neural network approach that utilizes radial basis functions (RBFs) to solve forward and inverse problems in the process of diffusion. The input layer incorporates multiquadric (MQ) RBFs, symbolizing the radial distance between the boundary points on the spacetime [...] Read more.
This study introduces a deep neural network approach that utilizes radial basis functions (RBFs) to solve forward and inverse problems in the process of diffusion. The input layer incorporates multiquadric (MQ) RBFs, symbolizing the radial distance between the boundary points on the spacetime boundary and the source points positioned outside the spacetime boundary. The output layer is the initial and boundary data given by analytical solutions of the diffusion equation. Utilizing the concept of the spacetime coordinates, the approximations for forward and backward diffusion problems involve assigning initial data on the bottom or top spacetime boundaries, respectively. As the need for discretization of the governing equation is eliminated, our straightforward approach uses only the provided boundary data and MQ RBFs. To validate the proposed method, various diffusion scenarios, including forward, backward, and inverse problems with noise, are examined. Results indicate that the method can achieve high-precision numerical solutions for solving diffusion problems. Notably, only 1/4 of the initial and boundary conditions are known, yet the method still yields precise results. Full article
(This article belongs to the Special Issue Numerical Analysis in Computational Mathematics)
►▼ Show Figures

Figure 1

23 pages, 1168 KiB  
Article
Numerical Analysis for Sturm–Liouville Problems with Nonlocal Generalized Boundary Conditions
by Chein-Shan Liu, Chih-Wen Chang and Chung-Lun Kuo
Mathematics 2024, 12(8), 1265; https://doi.org/10.3390/math12081265 - 22 Apr 2024
Viewed by 1260
Abstract
For the generalized Sturm–Liouville problem (GSLP), a new formulation is undertaken to reduce the number of unknowns from two to one in the target equation for the determination of eigenvalue. The eigenparameter-dependent shape functions are derived for using in a variable transformation, such [...] Read more.
For the generalized Sturm–Liouville problem (GSLP), a new formulation is undertaken to reduce the number of unknowns from two to one in the target equation for the determination of eigenvalue. The eigenparameter-dependent shape functions are derived for using in a variable transformation, such that the GSLP becomes an initial value problem for a new variable. For the uniqueness of eigenfunction an extra condition is imposed, which renders the right-end value of the new variable available; a derived implicit nonlinear equation is solved by an iterative method without using the differential; we can achieve highly precise eigenvalues. For the nonlocal Sturm–Liouville problem (NSLP), we consider two types of integral boundary conditions on the right end. For the first type of NSLP we can prove sufficient conditions for the positiveness of the eigenvalue. Negative eigenvalues and multiple solutions may exist for the second type of NSLP. We propose a boundary shape function method, a two-dimensional fixed-quasi-Newton method and a combination of them to solve the NSLP with fast convergence and high accuracy. From the aspect of numerical analysis the initial value problem of ordinary differential equations and scalar nonlinear equations are more easily treated than the original GSLP and NSLP, which is the main novelty of the paper to provide the mathematically equivalent and simpler mediums to determine the eigenvalues and eigenfunctions. Full article
(This article belongs to the Special Issue Numerical Analysis in Computational Mathematics)
►▼ Show Figures

Figure 1

22 pages, 349 KiB  
Article
New Memory-Updating Methods in Two-Step Newton’s Variants for Solving Nonlinear Equations with High Efficiency Index
by Chein-Shan Liu and Chih-Wen Chang
Mathematics 2024, 12(4), 581; https://doi.org/10.3390/math12040581 - 15 Feb 2024
Cited by 4 | Viewed by 1217
Abstract
In the paper, we iteratively solve a scalar nonlinear equation f(x)=0, where f∈C(I,R),x∈I⊂R, and I includes at least one real root r. [...] Read more.
In the paper, we iteratively solve a scalar nonlinear equation f(x)=0, where f∈C(I,R),x∈I⊂R, and I includes at least one real root r. Three novel two-step iterative schemes equipped with memory updating methods are developed; they are variants of the fixed-point Newton method. A triple data interpolation is carried out by the two-degree Newton polynomial, which is used to update the values of f′(r) and f″(r). The relaxation factor in the supplementary variable is accelerated by imposing an extra condition on the interpolant. The new memory method (NMM) can raise the efficiency index (E.I.) significantly. We apply the NMM to five existing fourth-order iterative methods, and the computed order of convergence (COC) and E.I. are evaluated by numerical tests. When the relaxation factor acceleration technique is combined with the modified Dzˇunic´’s memory method, the value of E.I. is much larger than that predicted by the paper [Kung, H.T.; Traub, J.F. J. Assoc. Comput. Machinery 1974, 21]. for the iterative method without memory. Full article
(This article belongs to the Special Issue Numerical Analysis in Computational Mathematics)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-6
Back to TopTop