Stability of solutions of delay functional integro-differential equations and their discretizations

The asymptotic stability and contractivity properties of solutions of a class of delay functional integro-differential equations are studied. Relevant properties of solutions of a particular equation as well as of a closely related linear version are discussed. The role of the integral delay operator is explained. The results obtained are used for explaining the analogous properties of numerical solutions generated by continuous Runge-Kutta or collocation methods.