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

Deadline for manuscript submissions: closed (31 December 2025) | Viewed by 17265

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Prof. Dr. Shufei Wu

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Guest Editor

Department of Statistics, Tamkang University, Taipei 251301, Taiwan
Interests: statistics
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Shou-Fu Tian

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Guest Editor

School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
Interests: partial differential equations
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Special Issue Information

Dear Colleagues,

Computational mathematics has became increasingly significant across diverse fields in science and engineering. This Special Issue aims to showcase recent research findings in computational mathematics and advanced numerical methods. The publication will encompass original and survey papers delving into analysis, modeling, control, and optimization. Contributions employing advanced computational mathematics and numerical methods, with applications spanning various realms of science, technology, engineering, and related disciplines, are encouraged and warmly welcomed.

Potential topics include, but are not limited to, the following:

Computational mathematics for data science;
Applied mathematics in optimization problems;
Signal processing and mathematical images;
Scientific computing and algorithms;
Numerical analysis for problems arising in various fields.

Prof. Dr. Shufei Wu
Prof. Dr. Shou-Fu Tian
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 250 words) can be sent to the Editorial Office for assessment.

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. Symmetry 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 mathematics for data science
applied mathematics in optimization problems
signal processing and mathematical images
scientific computing and algorithms
numerical analysis for problems arising in various fields

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Related Special Issue

Computational Mathematics and Its Applications in Numerical Analysis, 2nd Edition in Symmetry (1 article)

Published Papers (11 papers)

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Research

36 pages, 141661 KB

Open AccessArticle

Design Optimization of Eccentric Pole PM Motors Using the Bilinear Mapping Method

by Ali Jabbari and Frédéric Dubas

Symmetry 2026, 18(2), 368; https://doi.org/10.3390/sym18020368 - 16 Feb 2026

Viewed by 463

Abstract

The eccentric permanent-magnet (PM) pole technique is widely recognized as an effective technique for reducing cogging torque in surface-mounted PM motors (SMPMMs). This paper proposes a novel analytical approach based on bilinear mapping to determine the optimal PM reduction parameters. In this method, the outer surface of the PM and the stator inner bore are modeled as eccentric circles. Bilinear mapping is then used to transform a slotted stator bore into an equivalent slotless configuration with small slot-openings, allowing the optimal PM reduction to be identified. The key electromagnetic performance characteristics of SMPMMs—including torque, efficiency, mean air-gap flux density, and related parameters—are formulated as explicit mathematical functions of the PM reduction factor. The influence of the optimal PM reduction on both static and dynamic rotor eccentricity is also investigated. The results reveal that the bilinear mapping equations yield two distinct roots for the optimal PM reduction. Once the optimal values are known for a reference motor, those of other motors with different dimensions can be readily derived by scaling according to the ratio of the outer PM radii, without repeating the full calculation process. The proposed method is applicable to various SMPMM geometries, including radial, parallel, and bread-loaf configurations. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

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22 pages, 9604 KB

Open AccessArticle

Elliptic Functions and Advanced Analysis of Soliton Solutions for the Dullin–Gottwald–Holm Dynamical Equation with Applications of Mathematical Methods

by Syed T. R. Rizvi, Ibtehal Alazman, Nimra and Aly R. Seadawy

Symmetry 2025, 17(10), 1773; https://doi.org/10.3390/sym17101773 - 21 Oct 2025

Cited by 8 | Viewed by 993

Abstract

We studied traveling-wave solutions of the Dullin–Gottwald–Holm (DGH) equation via a sub-ODE construction. Under explicit algebraic constraints, the approach yielded closed-form families—bell-shaped, hyperbolic (

sech / \tanh

), Jacobi-elliptic function (JEF), Weierstrass-elliptic function (WEF), periodic, and rational—and classified their symmetry properties. Optical solitons [...] Read more.

sech / \tanh

), Jacobi-elliptic function (JEF), Weierstrass-elliptic function (WEF), periodic, and rational—and classified their symmetry properties. Optical solitons (bright and dark) arose as limiting cases of the elliptic solutions. We specified the parameter regimes that produced each profile and illustrated representative solutions with 2D/3D plots to highlight symmetry. The results provide a unified, reproducible procedure for generating solitary and periodic DGH waves and expand the catalog of exact solutions for this model. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

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27 pages, 4212 KB

Open AccessArticle

Artificial Neural Network Modeling of Darcy–Forchheimer Nanofluid Flow over a Porous Riga Plate: Insights into Brownian Motion, Thermal Radiation, and Activation Energy Effects on Heat Transfer

by Zafar Abbas, Aljethi Reem Abdullah, Muhammad Fawad Malik and Syed Asif Ali Shah

Symmetry 2025, 17(9), 1582; https://doi.org/10.3390/sym17091582 - 22 Sep 2025

Cited by 4 | Viewed by 1150

Abstract

Nanotechnology has become a transformative field in modern science and engineering, offering innovative approaches to enhance conventional thermal and fluid systems. Heat and mass transfer phenomena, particularly fluid motion across various geometries, play a crucial role in industrial and engineering processes. The inclusion of nanoparticles in base fluids significantly improves thermal conductivity and enables advanced phase-change technologies. The current work examines Powell–Eyring nanofluid’s heat transmission properties on a stretched Riga plate, considering the effects of magnetic fields, porosity, Darcy–Forchheimer flow, thermal radiation, and activation energy. Using the proper similarity transformations, the pertinent governing boundary-layer equations are converted into a set of ordinary differential equations (ODEs), which are then solved using the boundary value problem fourth-order collocation (BVP4C) technique in the MATLAB program. Tables and graphs are used to display the outcomes. Due to their significance in the industrial domain, the Nusselt number and skin friction are also evaluated. The velocity of the nanofluid is shown to decline with a boost in the Hartmann number, porosity, and Darcy–Forchheimer parameter values. Moreover, its energy curves are increased by boosting the values of thermal radiation and the Biot number. A stronger Hartmann number M decelerates the flow (thickening the momentum boundary layer), whereas increasing the Riga forcing parameter Q can locally enhance the near-wall velocity due to wall-parallel Lorentz forcing. Visual comparisons and numerical simulations are used to validate the results, confirming the durability and reliability of the suggested approach. By using a systematic design technique that includes training, testing, and validation, the fluid dynamics problem is solved. The model’s performance and generalization across many circumstances are assessed. In this work, an artificial neural network (ANN) architecture comprising two hidden layers is employed. The model is trained with the Levenberg–Marquardt scheme on reliable numerical datasets, enabling enhanced prediction capability and computational efficiency. The ANN demonstrates exceptional accuracy, with regression coefficients

R \approx 1.0

and the best validation mean squared errors of

8.52 \times 10^{- 10}

7.91 \times 10^{- 9}

, and

1.59 \times 10^{- 8}

for the Powell–Eyring, heat radiation, and thermophoresis models, respectively. The ANN-predicted velocity, temperature, and concentration profiles show good agreement with numerical findings, with only minor differences in insignificant areas, establishing the ANN as a credible surrogate for quick parametric assessment and refinement in magnetohydrodynamic (MHD) nanofluid heat transfer systems. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

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12 pages, 1173 KB

Open AccessCommunication

The Cramér–Von Mises Statistic for Continuous Distributions: A Monte Carlo Study for Calculating Its Associated Probability

by Lorentz Jäntschi

Symmetry 2025, 17(9), 1542; https://doi.org/10.3390/sym17091542 - 15 Sep 2025

Cited by 2 | Viewed by 1419

Abstract

The Cramér–von Mises (CM) statistic can assess the goodness-of-fit when the null distribution is independent of the underlying distribution, provided it is continuous, resulting in a universality that supports symmetry in its application and interpretation. Along with other order statistics, it serves in a battery of tests. A key element in its use is availability of the cumulative distribution function inverse for calculating the p-value. CM does not have an explicit formula for the cumulative distribution function. Here, a Monte–Carlo experiment was deployed to generate a large amount of data resembling CM. Furthermore, regression analysis was deployed, in order to obtain the dependence of the p-value as function of the statistic and of the sample size. For two cases, one assuming Beta distribution and the other assuming Cauchy distribution, an analysis using the CM statistic was conducted. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

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19 pages, 1819 KB

Open AccessArticle

Adaptive Optics Retinal Image Restoration Using Total Variation with Overlapping Group Sparsity

by Xiaotong Chen, Yurong Shi and Hongsun Fu

Symmetry 2025, 17(5), 660; https://doi.org/10.3390/sym17050660 - 26 Apr 2025

Viewed by 842

Abstract

Adaptive optics (AO)-corrected retina flood illumination imaging technology is widely used for investigating both structural and functional aspects of the retina. Given the inherent low-contrast nature of original retinal images, it is necessary to perform image restoration. Total variation (TV) regularization is an efficient regularization technique for AO retinal image restoration. However, a main shortcoming of TV regularization is its potential to experience the staircase effects, particularly in smooth regions of the image. To overcome the drawback, a new image restoration model is proposed for AO retinal images. This model utilizes the overlapping group sparse total variation (OGSTV) as a regularization term. Due to the structural characteristics of AO retinal images, only partial information regarding the PSF is known. Consequently, we have to solve a more complicated myopic deconvolution problem. To address this computational challenge, we propose an ADMM-MM-LAP method to solve the proposed model. First, we apply the alternating direction method of multiplier (ADMM) as the outer-layer optimization method. Then, appropriate algorithms are employed to solve the ADMM subproblems based on their inherent structures. Specifically, the majorization–minimization (MM) method is applied to handle the asymmetry OGSTV regularization component, while a modified version of the linearize and project (LAP) method is adopted to address the tightly coupled subproblem. Theoretically, we establish the complexity analysis of the proposed method. Numerical results demonstrate that the proposed model outperforms the existing state-of-the-art TV model across several metrics. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

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22 pages, 2491 KB

Open AccessArticle

Computational Analysis of the Comprehensive Lifetime Performance Index for Exponentiated Fréchet Lifetime Distribution Products with Multi-Components

by Shu-Fei Wu and Hsueh-Chien Yeh

Symmetry 2024, 16(8), 1060; https://doi.org/10.3390/sym16081060 - 16 Aug 2024

Viewed by 1762

Abstract

The lifetime performance index is commonly used in the manufacturing industry to evaluate the performance of the capabilities of the production process. For products with multiple components, the comprehensive lifetime performance index, which is a monotonically increasing function of the overall process yield, is used to relate to each individual lifetime performance index. For products where the lifetime of the ith component follows an exponentiated Fréchet lifetime distribution, we examine the maximum likelihood estimators for both the comprehensive and individual lifetime performance indices based on the progressive type I interval-censored samples, deriving their asymptotic distributions. By specifying the target level for the comprehensive lifetime performance index, we can set the desired level for individual indices. A testing procedure, using the maximum likelihood estimator as the test statistic, was developed to determine if the comprehensive lifetime performance index meets the target. Given that the lifetime distribution is asymmetric, this study pertains to asymmetrical probability distributions and their applications across diverse fields. We illustrate the power analysis of this testing procedure with figures and summarize key findings. Finally, we demonstrate the application of this testing algorithm with a practical example involving two components to verify if the overall production process achieves the assigned target level. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

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14 pages, 802 KB

Open AccessArticle

A Generalized Iterated Tikhonov Method in the Fourier Domain for Determining the Unknown Source of the Time-Fractional Diffusion Equation

by Bin Zheng, Junfeng Liu, Zhenyu Zhao, Zhihong Dou and Benxue Gong

Symmetry 2024, 16(7), 864; https://doi.org/10.3390/sym16070864 - 8 Jul 2024

Viewed by 1667

Abstract

In this paper, an inverse problem of determining a source in a time-fractional diffusion equation is investigated. A Fourier extension scheme is used to approximate the solution to avoid the impact on smoothness caused by directly using singular system eigenfunctions for approximation. A modified implicit iteration method is proposed as a regularization technique to stabilize the solution process. The convergence rates are derived when a discrepancy principle serves as the principle for choosing the regularization parameters. Numerical tests are provided to further verify the efficacy of the proposed method. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

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17 pages, 325 KB

Open AccessArticle

Solutions for the Nonlinear Mixed Variational Inequality Problem in the System

by Husain Gissy, Abdullah Ali H. Ahmadini and Salahuddin

Symmetry 2024, 16(7), 796; https://doi.org/10.3390/sym16070796 - 25 Jun 2024

Viewed by 1314

Abstract

Our paper proposes a system of nonlinear mixed variational inequality problems (SNMVIPs) on Banach spaces. Under suitable assumptions, using the K-Fan fixed point theorem and Minty techniques, we demonstrate that the solution set to the SNMVIP is nonempty, weakly compact, and unique. Additionally, we suggest a stability result for the SNMVIPs by perturbing the duality mappings. Furthermore, we present an optimal control problem that is governed by the SNMVIPs and show that it can be solved. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

23 pages, 1001 KB

Open AccessArticle

A Fast Method for the Off-Boundary Evaluation of Laplace Layer Potentials by Convolution Sums

by Wenchao Guan, Zhicheng Wang, Leqi Xue and Yueen Hou

Symmetry 2024, 16(6), 764; https://doi.org/10.3390/sym16060764 - 18 Jun 2024

Viewed by 1971

Abstract

In off-boundary computations of layer potentials, the near-singularities in integrals near the boundary presents challenges for conventional quadrature methods in achieving high precision. Additionally, the significant complexity of

O (n^{2})

interactions between n targets and n sources reduces the efficiency [...] Read more.

O (n^{2})

interactions between n targets and n sources reduces the efficiency of these methods. A fast and accurate numerical algorithm is presented for computing the Laplace layer potentials on a circle with a boundary described by a polar curve. This method can maintain high precision even when evaluating targets located at a close distance from the boundary. The radial symmetry of the integral kernels simplifies their description. By exploiting the polar form of the boundary and applying a one-dimensional exponential sum approximation along the radial direction, an approximation of layer potentials by the convolution sum is obtained. The algorithm uses FFT convolution to accelerate computation and employs a local quadrature to maintain accuracy for nearly singular terms. Consequently, it achieves spectral accuracy in regions outside of a sufficiently small neighborhood of the boundary and requires

O (n log n)

arithmetic operations. With the help of this algorithm, layer potentials can be efficiently evaluated on a computational domain. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

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13 pages, 237 KB

Open AccessArticle

An Efficient Solution of Multiplicative Differential Equations through Laguerre Polynomials

by Hatice Yalman Kosunalp, Selcuk Bas and Selahattin Kosunalp

Symmetry 2024, 16(6), 748; https://doi.org/10.3390/sym16060748 - 15 Jun 2024

Cited by 3 | Viewed by 1522

Abstract

The field of multiplicative analysis has recently garnered significant attention, particularly in the context of solving multiplicative differential equations (MDEs). The symmetry concept in MDEs facilitates the determination of invariant solutions and the reduction of these equations by leveraging their intrinsic symmetrical properties. This study is motivated by the need for efficient methods to address MDEs, which are critical in various applications. Our novel contribution involves leveraging the fundamental properties of orthogonal polynomials, specifically Laguerre polynomials, to derive new solutions for MDEs. We introduce the definitions of Laguerre multiplicative differential equations and multiplicative Laguerre polynomials. By applying the power series method, we construct these multiplicative Laguerre polynomials and rigorously prove their basic properties. The effectiveness of our proposed solution is validated through illustrative examples, demonstrating its practical applicability and potential for advancing the field of multiplicative analysis. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

19 pages, 366 KB

Open AccessArticle

A New Adaptive Levenberg–Marquardt Method for Nonlinear Equations and Its Convergence Rate under the Hölderian Local Error Bound Condition

by Yang Han and Shaoping Rui

Symmetry 2024, 16(6), 674; https://doi.org/10.3390/sym16060674 - 30 May 2024

Cited by 7 | Viewed by 2240

Abstract

The Levenberg–Marquardt (LM) method is one of the most significant methods for solving nonlinear equations as well as symmetric and asymmetric linear equations. To improve the method, this paper proposes a new adaptive LM algorithm by modifying the LM parameter, combining the trust region technique and the non-monotone technique. It is interesting that the new algorithm is constantly optimized by adaptively choosing the LM parameter. To evaluate the effectiveness of the new algorithm, we conduct tests using various examples. To extend the convergence results, we prove the convergence of the new algorithm under the Hölderian local error bound condition rather than the commonly used local error bound condition. Theoretical analysis and numerical results show that the new algorithm is stable and effective. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

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