Stability properties of quadrature-based approximations for integral equations with delay terms
Eleonora Messina1, Claudia Panico1
1Department of Mathematics and Applications, University of Naples Federico Ⅱ, via Cintia, I-80126 Naples, Italy.
Mathematical Biosciences and Engineering : MBE
|August 2, 2026
Summary
This study analyzes linear integral equations with discrete and distributed delays, common in biological modeling and control theory. Numerical methods are used to ensure discrete models accurately reflect the stability of continuous systems.
Area of Science:
- Numerical Analysis
- Applied Mathematics
- Mathematical Biology
Background:
- Linear integral equations with discrete and distributed delays are crucial in modeling biological systems and control theory.
- Understanding the stability of these continuous models is essential for reliable predictions and system design.
Purpose of the Study:
- To investigate the stability properties of discretized linear integral equations with both discrete and bounded distributed delays.
- To establish conditions under which numerical methods preserve the stability of the original continuous equations.
Main Methods:
- Discretization of integral equations using quadrature-based numerical methods.
- Stability analysis of the resulting discrete schemes.
- Derivation of sufficient conditions for stability preservation.
Main Results:
- The study provides a framework for analyzing the stability of discretized delay integral equations.
- Sufficient conditions were derived to guarantee that the discrete formulation accurately reflects the stability of the continuous problem.
- This ensures the reliability of numerical simulations for systems with delays.
Conclusions:
- Quadrature-based discretization methods can effectively preserve the stability of linear integral equations with discrete and distributed delays.
- The derived conditions offer practical guidelines for selecting appropriate numerical methods in applications.
- This work contributes to the robust mathematical modeling of complex dynamic systems.
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