Submission Deadline: 30 June 2027 View: 726 Submit to Special Issue
Prof. Dr. Higinio Ramos
Email: higra@usal.es
Affiliation: Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, Salamanca, Spain
Research Interests: numerical analysis, adaptive stepsize algorithms, numerical solution of differential equations, Chebyshev approximations, block methods, computational mathematics
Dr. Chandru Muthusamy
Email: chandru.m@vit.ac.in
Affiliation: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India
Research Interests: numerical analysis, singularly perturbed problems, numerical solutions of differential equations of integer and fractional orders, finite and virtual element methods, computational mathematics, boundary element methods, pattern formation in chemical and biological systems and water wave phenomena
Differential equations are the mathematical foundation for modelling physical systems arising in science and engineering, including fluid dynamics, heat transfer, wave propagation, electromagnetics, materials science, biological systems, and other complex dynamical processes. The increasing complexity of these models, involving nonlinearities, multiscale phenomena, stochastic effects, and high-dimensional parameter spaces, has created a growing demand for advanced numerical methods and intelligent computational techniques capable of delivering accurate, efficient, and reliable solutions.
Recent advances in scientific machine learning (SciML) have opened new opportunities for solving differential equations by integrating mathematical models with data-driven approaches. Emerging methodologies such as physics-informed neural networks (PINNs), neural operators, operator learning, hybrid physics-based machine learning, surrogate modelling, and reduced-order models are transforming computational approaches for forward and inverse problems in physical systems. These techniques complement classical numerical methods by improving computational efficiency, accelerating simulations, enabling data assimilation, and enhancing predictive capabilities while preserving physical consistency.
This Special Issue aims to provide an international platform for publishing high-quality original research and review articles on recent developments in numerical methods and machine learning techniques for differential equations and physical systems. Contributions presenting rigorous mathematical analysis, novel computational algorithms, and applications to realistic physical models are particularly encouraged. The issue seeks to strengthen the synergy between numerical analysis, scientific machine learning, and computational modelling, promoting interdisciplinary research among mathematicians, computational scientists, engineers, and physicists.
Topics of Interest include, but are not limited to:
· Numerical methods for ordinary, partial, delay, stochastic, and fractional differential equations;
· High-order, adaptive, and structure-preserving numerical algorithms;
· Finite difference, finite element, finite volume, spectral, meshless, and hybrid numerical methods;
· Scientific machine learning, including physics-informed neural networks (PINNs) and neural operators;
· Hybrid physics-based and data-driven computational methods;
· Reduced-order modeling, surrogate modeling, and operator learning;
· Inverse problems, parameter estimation, data assimilation, and uncertainty quantification;
· Numerical and machine learning methods for nonlinear, multiscale, and multiphysics systems;
· Computational modeling and simulation of physical systems (e.g., fluid dynamics, solid mechanics, heat transfer, electromagnetics, and wave propagation);
· Explainable AI, optimization, and intelligent computing for differential equations and physical systems.
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