Numerical stability analysis of steady state solutions of integral equations with distributed delays (Q596555)

The authors consider the delay integral equation \[ y(t)=a\int_{t-\tau}^t K(t-\xi)y(\xi)d\xi \] under a discrete scheme based on Lagrange interpolation and a Gauss-Legendre quadrature rule. The aim of the paper is to establish conditions under which the true stability of the underlying equation is preserved in the discrete scheme. The paper is structured as follows: after an initial introduction, the authors describe their discrete scheme, they review the stability properties of the zero solution of the integral equation and deduce results relating the properties of the zero solution of the discrete analogue. Their detailed investigations lead to conjectures about the preservation of stability in discrete analogue equation. The results of numerical experiments are reported.