The transform is a delay integral equation (DIE), where y ∈ ℜ, a ∈ ℜ, and K(&xgr;) > 0 is a bounded analytic kernel function defined on the interval [0, &tgr;].

In this work, the authors study the numerical stability of scalar DIEs, with constant and nonconstant kernel function in equation (1). First, the integral is approximated using a quadrature method based on Lagrange interpolation and Gauss-Legendre quadrature, then the properties of this discretization are investigated in the context of stability analysis. Some numerical results are provided on computing the stability of equation (1).