A Numerical Algorithm for Approximating the Periodic Solution of Volterra Integral Equation with Delay

In this paper, a new approach based on several known numerical algorithms for a class of Volterra integral equations with constant delay is presented. First, using Fourier transform, we approximatethe solution for Volterra integral equation with periodic solution. To approximate the definite integrals we use Gauss-Legendre quadrature rules. Next, utilizing Newton’s method we compute the Fourier coefficients. The various numerical results show the efficiency and performance of the proposed algorithm.