RIMNI SPECIAL ISSUE - Iterative Methods for Solving Complex Systems: Linear, Nonlinear, Complementarity, and Fractional Differential Equations

Deadline Date: 31 December 2026

This special issue aims to present recent advances in iterative methods for solving complex systems, including linear and nonlinear equations, complementarity problems, absolute value equations, and fractional differential equations (FDEs). The focus is on bridging theory and practice, addressing challenges posed by large-scale, nonlocal, and memory-dependent problems.

Iterative techniques remain essential where direct solvers fail due to size, nonlinearity, or nonsmooth structure. Contributions are welcome on novel algorithms, convergence and stability analyses, error estimates, and acceleration strategies. Particular emphasis is placed on iterative methods for FDEs—such as predictor-corrector schemes, finite difference iterations, spectral techniques, and Newton-type solvers—which must handle weakly singular kernels and long-term memory.

Applications span scientific computing, engineering (viscoelasticity, anomalous diffusion), economics, control theory, biology, and data-driven modeling. Hybrid approaches, machine learning-integrated iterative solvers, and large-scale numerical implementations are also encouraged.

Topics of interest for the special issue include, but are not limited to, the following:

General iterative methods for solving linear and nonlinear systems;

Iterative solutions forcomplementarity problems;

Iterative algorithms for absolute value equations;

Iterative methods for fractional differential equations (FDEs);

Numerical iterative schemes for fractional boundary and initial value problems;

Convergence and stability analysis of iterative methods for fractional systems;

Hybrid and accelerated iterative techniques for complex systems;

Convergence and stability analysis of iterative processes;

Optimization and efficiency in iterative methods for large-scale systems;

Applications in scientific computing, engineering, economics, biology, and beyond;

Iterative approaches for nonlinear optimization problems;