Special issue "Numerical Analysis of Differential Equations with Real-world Applications"

Numerical analysis of differential equations plays an essential role in addressing a wide range of challenging problems in science and engineering, where analytical solutions are often unavailable due to nonlinearity, complex geometries, multiscale effects, or uncertainty.This Special Issue, Numerical Analysis of Differential Equations, was conceived as a platform for original contributions that develop, analyze, and apply robust numerical methods, while advancing the theoretical understanding and computational reliability of models arising from ordinary, partial, delay, fractional, and integro-differential equations.The papers published in this Special Issue reflect this dual objective of methodological innovation and rigorous analysis.They span stochastic and deterministic differential equations, singular perturbation theory, delay and fractional-order systems, soliton dynamics, and energy-stable numerical schemes, together with control-theoretic and stability analyses for complex dynamical models.The contributions address a broad spectrum of problems, ranging from nonlinear wave propagation and chaos in dispersive equations to integro-differential formulations, oscillation criteria, and high-order numerical algorithms for stiff and non-smooth systems.Despite this diversity, the papers share a common perspective: carefully designed numerical methods, supported by rigorous analytical frameworks, are essential for accurately capturing multiscale dynamics, ensuring stability and convergence, and enabling reliable simulation, analysis, and control of complex systems governed by differential equations.In the first group of papers, the emphasis is on nonlinear wave dynamics and soliton behaviour