A numerical investigation on the asymptotic behavior of discrete Volterra equations with two delays (Q618711)

The authors provide a numerical investigation on the asymptotic behavior of discrete Volterra equations with two delays. First they provide the properties of the continuous solution and then prove a new result on global asymptotic stability of the nontrivial equilibrium. Later they consider a numerical method of direct quadrature type and look for conditions on the step size \(h\) of a direct quadrature method that lead to a numerical solution which mimic the the behavior of continuous one. The authors discuss the parallelism between the behaviors of the analytical and the numerical solution. Numerical examples are given.