Mathematical Modeling, Computational Methods, and AI-Driven Applications in Industrial and Applied Mathematics

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: 31 July 2027 | Viewed by 625

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Guest Editor
1. Control and Energy Management Laboratory, National School of Engineering of Sfax, University of Sfax, Sfax 3038, Tunisia
2. Higher Institute of Applied Sciences and Technology of Kairouan, University of Kairouan, Kairouan 3100, Tunisia
Interests: mathematical modeling; nonlinear systems; fractional-order systems; stability and control; signal analysis; AI-enabled optimization
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1. Mathematics Education Section, Faculty of Education and Arts, Sohar University, P.O. Box 44, Sohar 311, Oman
2. Department of Mathematics, Faculty of Sciences of Sfax, Sfax University, Sfax 3029, Tunisia
Interests: differential equations; fractional calculus; control theory; dynamical systems; stability analysis
Special Issues, Collections and Topics in MDPI journals

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Department of Mathematics, Institut Galilée, University of Paris 13, 93430 Villetaneuse, France
Interests: mathematical modeling; differential equations; fractional calculus; control theory; dynamical systems; stability analysis

Special Issue Information

Dear Colleagues,

Mathematical modeling and computational methods are fundamental for solving contemporary problems in engineering, natural sciences, medicine, economics, and technology. This Special Issue aims to collect high-quality contributions presented by, or aligned with, the International Conference of Industrial and Applied Mathematics (ICoIAM 2026, https://iciam.net/), focusing on rigorous mathematical developments and computational techniques with clear applications. We welcome original research and review articles on differential equations and dynamical systems, fractional calculus, numerical analysis and simulation, optimization and control, finite element and integral equation methods, inverse problems, stochastic modeling, artificial intelligence and machine learning for applied mathematics, computational mechanics, signal and image processing, and data-driven approaches to complex systems. Particular interest will be given to works that combine theoretical analysis with reproducible computational experiments, algorithms, simulations, or real-world case studies. The Special Issue seeks to strengthen interaction between mathematicians, engineers, computer scientists, and applied researchers, and to showcase emerging tools for modeling, prediction, control, and decision-making in industrial and scientific applications.

Dr. Omar Naifar
Dr. Abdellatif Ben Makhlouf
Dr. Lassaad Mchiri
Guest Editors

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Keywords

  • differential equations
  • dynamical systems
  • fractional calculus
  • numerical analysis

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Published Papers (1 paper)

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Research

23 pages, 901 KB  
Article
A Robust High-Order Haar Wavelet Collocation Method for Linear and Nonlinear Delay Differential Equations: Theoretical Analysis and Numerical Validation
by Naveed Khan, Muhammad Asif, Muhammad Ahsan, Naveed Ullah and Ioan-Lucian Popa
Math. Comput. Appl. 2026, 31(4), 162; https://doi.org/10.3390/mca31040162 - 14 Aug 2026
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Abstract
Delay differential equations form a distinct class of differential equations in which the derivative of the dependent variable depends on its value at an earlier time. This unique structure makes them particularly suitable for modeling phenomena in areas such as population dynamics, epidemiology, [...] Read more.
Delay differential equations form a distinct class of differential equations in which the derivative of the dependent variable depends on its value at an earlier time. This unique structure makes them particularly suitable for modeling phenomena in areas such as population dynamics, epidemiology, and the spread or control of diseases. In this study, a high-order Haar wavelet collocation method (HoHWCM) is proposed for the numerical solution of second-order delay differential equations (SoDDEs). The delay term is approximated using a Taylor expansion, transforming the SoDDE into a standard second-order differential equation (SoDE). The nonlinear terms are linearized through an innovative Taylor series-based approach, which also serves as an efficient iterative scheme. The resulting SoDE is then discretized using Haar wavelet basis functions, yielding a system of linear algebraic equations that is solved iteratively. This strategy eliminates the need for Newton’s or Broyden’s methods, thereby reducing computational cost and improving time efficiency. A variety of linear and nonlinear benchmark problems are solved to evaluate the accuracy and efficiency of the proposed method. Comparative results with established approaches from the literature demonstrate that the HoHWCM achieves higher accuracy, faster convergence, and reduced computational time, making it a highly effective alternative for solving such problems. Full article
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