Special Issue: Numerical Analysis and Computational Mathematics: Recent Advances and Emerging Applications

2026-03-05

Summary

Differential equations—of integer and fractional order—play a central role in modelling a wide spectrum of phenomena arising in science and engineering, including diffusion processes, electrodynamics, control systems, structural mechanics, fluid flow, and biophysics. These models often lead to ordinary and partial differential equations that may be linear or nonlinear, singular or singularly perturbed, deterministic or stochastic. In many practical situations, analytical solutions are either unavailable or extremely difficult to obtain, particularly when dealing with complex geometries, multiscale structures, or nonlinear interactions.

As a result, the development of robust, accurate, and efficient numerical methods has become an essential pillar of modern applied mathematics. Recent advances in computational mathematics—such as high-order discretization techniques, adaptive algorithms, virtual element methods, structure-preserving schemes, and data-driven computational strategies—have significantly enhanced our ability to analyze and simulate complex dynamical systems in real time.

This Special Issue aims to highlight the latest research advances and significant achievements in Numerical Analysis and Computational Mathematics, with particular emphasis on innovative numerical methodologies, rigorous theoretical analysis, and impactful applications in science and engineering. The issue will serve as a platform for researchers to present cutting-edge developments that bridge theory, computation, and real-world applications.

Scope and Objectives

The primary objectives of this Special Issue are:

To promote recent theoretical developments in numerical analysis.
To present efficient and stable computational algorithms for differential equations.
To explore emerging challenges in fractional, stochastic, and nonlinear systems.
To connect rigorous mathematical analysis with practical scientific computing applications.
To encourage interdisciplinary contributions linking mathematics, physics, and engineering.

Key Topics

The Special Issue will include, but is not limited to, the following topics:

Numerical analysis for ordinary and partial differential equations
Scientific computing for dynamical systems
Robust and high-order computational methods
Integer and fractional order differential equations
Singular and singularly perturbed problems
Applications of stochastic differential equations
Bifurcation theory and dynamical systems analysis
Control theory and optimization
Nonlinear dynamics and pattern formation
Fluid dynamics and computational mechanics
Water wave interaction problems
Virtual element and finite element methods
Structure-preserving and energy-stable numerical schemes

Expected Contributions

We invite original research articles, review papers, and short communications presenting:

Novel numerical algorithms with theoretical error analysis
Convergence and stability analysis of computational schemes
Multiscale and multiphysics modelling approaches
Efficient solvers for large-scale computational problems
Real-time simulations and high-performance computing applications
Comparative studies of modern numerical techniques

Target Audience

This Special Issue will be of interest to researchers and practitioners in: Applied Mathematics Computational Science and Engineering Numerical Analysis Mathematical Modelling Scientific Computing 6. Significance By focusing on both theoretical foundations and computational innovations, this Special Issue will contribute to advancing modern numerical methodologies and their applications to complex real-world systems. It will provide a comprehensive overview of emerging trends and future directions in Numerical Analysis and Computational Mathematics.

Lead Guest Editor

Higinio Ramos

Affiliation: Full Professor, Department of Mathematics, University of Salamanca, Spain.

Research Interests: Numerical analysis, adaptive stepsize algorithms, numerical solution of differential equations, Chebyshev approximations, block methods, computational mathematics.

E-Mail: higra@usal.es

Website: https://produccioncientifica.usal.es/investigadores/56393/colaboracion

Co-Guest Editor

Chandru Muthusamy

Affiliation: Assistant Professor, 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.

E-Mail: leochandru@gmail.com(primary), chandru.m@vit.ac.in(secondary)

Website: https://research.vit.ac.in/researcher/chandru-m

All manuscripts submitted to the Special Issue will follow the same rigorous peer-review process as regular submissions and will be published in regular issues of CM.

Important Dates

Starting Date of Submission: 10 March 2026

Submission Deadline: 09 March 2027

Submission Information

Submit it online: http://ojs.wiserpub.com/index.php/CM/user/register

Or send it to the email address: mark@wiserpub.com