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Mathematics
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Mathematical Modelling and Computational Methods in Real-World Applications
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Mathematical Modelling and Computational Methods in Real-World Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 31 January 2027 | Viewed by 5560

Special Issue Editors

Dr. Guodong Li

E-Mail Website
Guest Editor
1. School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541002, China
2. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541002, China
3. Center for Applied Mathematics of Guangxi (GUET), Guilin 541002, China
Interests: Interests: fractals and chaos; chaotic system design; memristors; image–audio encryption algorithms; chaotic circuit design
Special Issues, Collections and Topics in MDPI journals
Dr. Maofa Wang

E-Mail Website
Guest Editor
School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
Interests: meta learning; artificial intelligence; deep learning

Special Issue Information

Dear Colleagues,

In today’s complex and data-driven world, the application of mathematical modelling and computational methods is essential for solving real-world challenges across diverse fields. From optimising business operations and predicting economic trends to securing digital infrastructure and advancing scientific research, mathematical and computational tools provide the foundation for innovation and informed decision-making. By integrating rigorous theoretical frameworks with practical computational techniques, researchers and practitioners can develop robust solutions that address dynamic problems in management, finance, technology, and beyond. This Special Issue aims to highlight cutting-edge methodologies, theoretical advances, and impactful applications that demonstrate how mathematical modelling and computational approaches can be leveraged to tackle contemporary issues in real-world contexts.

The scope of this Special Issue covers a broad spectrum of topics related to mathematical modelling and computational methods in practical settings. Research areas considered for publication may include, but are not limited to, the following:

  • Mathematical models in management and decision sciences, including optimisation and resource allocation; 
  • Numerical methods for solving complex systems in engineering, physics, and applied sciences; 
  • Integration of machine learning with mathematical modelling for predictive analytics and automation; 
  • Nonlinear theory applied to real-world dynamic systems in ecology, biology, and social sciences; 
  • Economic mathematics for modelling market behaviour, policy analysis, and development strategies; 
  • Financial mathematics for risk management, derivative pricing, and quantitative finance; 
  • Mathematical approaches to information security, including cryptography and secure system design; 
  • Optimisation algorithms in logistics, supply chain management, and operational research; 
  • Statistical prediction models in public health, climate science, and business forecasting. 

We invite contributions that explore these and related themes, offering new insights and scalable solutions grounded in mathematical and computational excellence.

Dr. Guodong Li
Dr. Maofa Wang
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. 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

  • information security
  • machine learning
  • mathematical models
  • security and privacy
  • privacy-enhancing technologies

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

Published Papers (8 papers)

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Research

17 pages, 459 KB  
Article
A Linear Fully Discrete Spectral Scheme for the Time Fractional Allen–Cahn Equation
by Xiaoli Li, Wenping Chen, Qingqiong Li, Lihua Jiang and Tianyi Liu
Mathematics 2026, 14(6), 1006; https://doi.org/10.3390/math14061006 - 16 Mar 2026
Viewed by 244
Abstract
This paper considers the numerical approximation of the time fractional Allen–Cahn equation with initial and periodic boundary conditions, and a linear fully discrete scheme is constructed with the finite difference method in time and the Fourier spectral method in space. Based on a [...] Read more.
This paper considers the numerical approximation of the time fractional Allen–Cahn equation with initial and periodic boundary conditions, and a linear fully discrete scheme is constructed with the finite difference method in time and the Fourier spectral method in space. Based on a temporal–spatial error splitting argument, the boundedness of numerical solutions in the L∞ norm is rigorously proved and the unconditional convergence of the proposed scheme is obtained. Numerical examples illustrate the theoretical results. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Real-World Applications)
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14 pages, 363 KB  
Article
The Legendre Spectral Method for Solving the Nonlinear Time-Fractional Convection-Diffusion Equations
by Guangfeng Lu, Lihua Jiang, Wenping Chen, Qingping Cheng and Xinyue Wang
Mathematics 2026, 14(5), 903; https://doi.org/10.3390/math14050903 - 6 Mar 2026
Viewed by 357
Abstract
In this paper, the nonlinear time-fractional convection-diffusion equations are solved by the Legendre spectral method. The Caputo time-fractional derivative is discretized by the L2–1σ scheme. A priori estimates of the fully discrete scheme are derived, and the existence and [...] Read more.
In this paper, the nonlinear time-fractional convection-diffusion equations are solved by the Legendre spectral method. The Caputo time-fractional derivative is discretized by the L2–1σ scheme. A priori estimates of the fully discrete scheme are derived, and the existence and uniqueness of the numerical solution are analyzed. It is rigorously proved that the fully discrete scheme is unconditionally stable, and the convergence order of the numerical scheme is O(N1−m+τ2). Finally, numerical results are presented to verify the theoretical analysis. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Real-World Applications)
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18 pages, 318 KB  
Article
Fourier Spectral Method for Nonlinear Time-Fractional Sine-Gordon Equations
by Luyan Zhen, Lihua Jiang and Wenping Chen
Mathematics 2026, 14(5), 873; https://doi.org/10.3390/math14050873 - 5 Mar 2026
Viewed by 225
Abstract
In this paper, the nonlinear time-fractional Sine-Gordon equation is investigated via the Fourier spectral method. The time-fractional derivative is approximated by the L1 approximation scheme, and the spatial component is discretized using the Fourier spectral method. The existence and uniqueness of the numerical [...] Read more.
In this paper, the nonlinear time-fractional Sine-Gordon equation is investigated via the Fourier spectral method. The time-fractional derivative is approximated by the L1 approximation scheme, and the spatial component is discretized using the Fourier spectral method. The existence and uniqueness of the numerical solution are proven, and the stability and convergence of the proposed method are analyzed, respectively. Theoretical results are validated by numerical experiment. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Real-World Applications)
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18 pages, 6910 KB  
Article
Construction of a New Discrete Chaotic Mapping Based on the Robust Chaos Theorem
by Liyan Hua, Xiangkun Chen, Guodong Li, Bo Tang and Wenxia Xu
Mathematics 2026, 14(5), 797; https://doi.org/10.3390/math14050797 - 26 Feb 2026
Viewed by 401
Abstract
Chaotic systems serve as fundamental pseudo-random sequence generators in encryption algorithms and play a vital role in communication security. However, most current research still focus on the classical Logistic chaotic map, making it vulnerable to targeted attacks. To address this issue, this paper [...] Read more.
Chaotic systems serve as fundamental pseudo-random sequence generators in encryption algorithms and play a vital role in communication security. However, most current research still focus on the classical Logistic chaotic map, making it vulnerable to targeted attacks. To address this issue, this paper proposes a general construction method for a class of cubic chaotic maps over the real number field and proves the existence of chaos based on the robust chaos criterion for S-unimodal maps. Furthermore, by integrating the proposed cubic chaotic map with the infinite folding map, a new one-dimensional discrete chaotic map is developed. Dynamical analysis demonstrates that, compared with the infinite folding map and the Logistic map, the newly constructed map exhibits stronger chaotic behavior and more stable complexity, showing superior potential for practical applications in secure communications. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Real-World Applications)
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21 pages, 7919 KB  
Article
Design of a Four-Dimensional Discrete Chaotic Image Encryption Algorithm Based on Dynamic Adjacency Matrix
by Hua Cai, Wenxia Xu, Ziwei Zhou and Guodong Li
Mathematics 2026, 14(4), 616; https://doi.org/10.3390/math14040616 - 10 Feb 2026
Viewed by 474
Abstract
Chaotic systems, with their characteristics of high sensitivity to initial conditions, pseudo-randomness, and ergodicity, provide high-quality pseudo-random sequences. Graph theory, through mechanisms such as vertex mapping, path traversal, and graph partitioning, can enhance data confusion and diffusion capabilities. This research designs an image [...] Read more.
Chaotic systems, with their characteristics of high sensitivity to initial conditions, pseudo-randomness, and ergodicity, provide high-quality pseudo-random sequences. Graph theory, through mechanisms such as vertex mapping, path traversal, and graph partitioning, can enhance data confusion and diffusion capabilities. This research designs an image encryption method that combines graph theory and chaotic systems. Firstly, a four-dimensional discrete chaotic system is constructed based on the Hénon map, and its chaotic characteristics and high complexity over a wide range of parameters and initial values are verified using Lyapunov exponents and permutation entropy. Secondly, an encryption framework based on a dynamic adjacency matrix from graph theory is proposed: image pixels are mapped to a dynamic graph structure, and sparse adjacency matrices are generated using chaotic sequences to achieve pixel scrambling based on graph traversal; then, chaotic sequences are used for feedback diffusion with pixel values to enhance the confusion effect. Multiple sets of experiments verify its effectiveness and robustness in terms of key sensitivity, statistical analysis, resistance to differential attacks, and resistance to cropping attacks. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Real-World Applications)
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10 pages, 3514 KB  
Article
General Construction Method and Proof for a Class of Quadratic Chaotic Mappings
by Wenxia Xu, Xiangkun Chen, Ziwei Zhou, Guodong Li and Xiaoming Song
Mathematics 2025, 13(15), 2409; https://doi.org/10.3390/math13152409 - 26 Jul 2025
Cited by 2 | Viewed by 632
Abstract
The importance of chaotic systems as the main pseudo-random cryptographic generator of encryption algorithms in the field of communication secrecy cannot be overstated, but in practical applications, researchers often choose to build upon traditional chaotic maps, such as the logistic map, for study [...] Read more.
The importance of chaotic systems as the main pseudo-random cryptographic generator of encryption algorithms in the field of communication secrecy cannot be overstated, but in practical applications, researchers often choose to build upon traditional chaotic maps, such as the logistic map, for study and application. This approach provides attackers with more opportunities to compromise the encryption scheme. Therefore, based on previous results, this paper theoretically investigates discrete chaotic mappings in the real domain, constructs a general method for a class of quadratic chaotic mappings, and justifies its existence based on a robust chaos determination theorem for S single-peaked mappings. Based on the theorem, we construct two chaotic map examples and conduct detailed analysis of their Lyapunov exponent spectra and bifurcation diagrams. Subsequently, comparative analysis is performed between the proposed quadratic chaotic maps and the conventional logistic map using the 0–1 test for chaos and SE complexity metrics, validating their enhanced chaotic properties. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Real-World Applications)
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22 pages, 501 KB  
Article
Identification of a Time-Dependent Source Term in Multi-Term Time–Space Fractional Diffusion Equations
by Yushan Li, Yuxuan Yang and Nanbo Chen
Mathematics 2025, 13(13), 2123; https://doi.org/10.3390/math13132123 - 28 Jun 2025
Cited by 1 | Viewed by 738
Abstract
This paper investigates the inverse problem of identifying a time-dependent source term in multi-term time–space fractional diffusion Equations (TSFDE). First, we rigorously establish the existence and uniqueness of strong solutions for the associated direct problem under homogeneous Dirichlet boundary conditions. A novel implicit [...] Read more.
This paper investigates the inverse problem of identifying a time-dependent source term in multi-term time–space fractional diffusion Equations (TSFDE). First, we rigorously establish the existence and uniqueness of strong solutions for the associated direct problem under homogeneous Dirichlet boundary conditions. A novel implicit finite difference scheme incorporating matrix transfer technique is developed for solving the initial-boundary value problem numerically. Regarding the inverse problem, we prove the solution uniqueness and stability estimates based on interior measurement data. The source identification problem is reformulated as a variational problem using the Tikhonov regularization method, and an approximate solution to the inverse problem is obtained with the aid of the optimal perturbation algorithm. Extensive numerical simulations involving six test cases in both 1D and 2D configurations demonstrate the high effectiveness and satisfactory stability of the proposed methodology. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Real-World Applications)
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37 pages, 6550 KB  
Article
Multiphase Transport Network Optimization: Mathematical Framework Integrating Resilience Quantification and Dynamic Algorithm Coupling
by Linghao Ren, Xinyue Li, Renjie Song, Yuning Wang, Meiyun Gui and Bo Tang
Mathematics 2025, 13(13), 2061; https://doi.org/10.3390/math13132061 - 21 Jun 2025
Cited by 2 | Viewed by 1515
Abstract
This study proposes a multi-dimensional urban transportation network optimization framework (MTNO-RQDC) to address structural failure risks from aging infrastructure and regional connectivity bottlenecks. Through dual-dataset validation using both the Baltimore road network and PeMS07 traffic flow data, we first develop a traffic simulation [...] Read more.
This study proposes a multi-dimensional urban transportation network optimization framework (MTNO-RQDC) to address structural failure risks from aging infrastructure and regional connectivity bottlenecks. Through dual-dataset validation using both the Baltimore road network and PeMS07 traffic flow data, we first develop a traffic simulation model integrating Dijkstra’s algorithm with capacity-constrained allocation strategies for guiding reconstruction planning for the collapsed Francis Scott Key Bridge. Next, we create a dynamic adaptive public transit optimization model using an entropy weight-TOPSIS decision framework coupled with an improved simulated annealing algorithm (ISA-TS), achieving coordinated suburban–urban network optimization while maintaining 92.3% solution stability under simulated node failure conditions. The framework introduces three key innovations: (1) a dual-layer regional division model combining K-means geographical partitioning with spectral clustering functional zoning; (2) fault-tolerant network topology optimization demonstrated through 1000-epoch Monte Carlo failure simulations; (3) cross-dataset transferability validation showing 15.7% performance variance between Baltimore and PeMS07 environments. Experimental results demonstrate a 28.7% reduction in road network traffic variance (from 42,760 to 32,100), 22.4% improvement in public transit path redundancy, and 30.4–44.6% decrease in regional traffic load variance with minimal costs. Hyperparameter analysis reveals two optimal operational modes: rapid cooling (rate = 0.90) achieves 85% improvement within 50 epochs for emergency response, while slow cooling (rate = 0.99) yields 12.7% superior solutions for long-term planning. The framework establishes a new multi-objective paradigm balancing structural resilience, functional connectivity, and computational robustness for sustainable smart city transportation systems. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Real-World Applications)
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