On the numerical solution of nonlinear systems of Volterra integro-differential equations with delay arguments

Particular cases of nonlinear systems of delay Volterra integro-differential equations (denoted by DVIDEs) with constant delay τ > 0, arise in mathematical modelling of ‘predator–prey’ dynamics in Ecology. In this paper, we give an analysis of the global convergence and local superconvergence properties of piecewise polynomial collocation for systems of this type. Then, from the perspective of applied mathematics, we consider the Volterra’s integro-differential system of ‘predator–prey’ dynamics arising in Ecology. We analyze the numerical issues of the introduced collocation method applied to the ‘predator–prey’ system and confirm that we can achieve the expected theoretical orders of convergence.