The numerical treatment of Volterra integro-differential equations with unbounded delay

摘要

Initial-value problems for ordinary and partial Volterra integro-differential equations with infinite (and finite) delay arise in the mathematical modelling of various physical and biological phenomena. In this paper we give a survey of some recent developments in the numerical treatment of such functional equations, with the focus being on equations with infinite delay. In addition, we will discuss a number of numerical aspects that are not yet understood well.