Numerical stability analysis of steady state solutions of integral equations with distributed delays Original Research Article

This paper concerns the numerical stability analysis of scalar delay integral equations (DIEs). We discretize a DIE using a quadrature method based on Lagrange interpolation and a Gauss–Legendre quadrature rule. We investigate properties of this discretization in the context of stability analysis. Conditions are obtained under which the discretized equation retains certain stability properties of the original equation. Results of numerical experiments on computing stability of DIEs are presented.