Verified Integration of Differential Equations with Discrete Delay

Many dynamic system models in population dynamics, physics and control involve temporally delayed state information such a way that the evolution of future trajectories depends not only on current as initial condition but also some previous state. In technical systems, phenomena result, for example, from mass transport incompressible fluids through finitely long pipelines, combustible material coal power plants via conveyor belts, or processing delays. Under assumption continuous corresponding delays can be treated either constant fixed, uncertain bounded even state-dependent. this paper, we restrict discussion to first two classes provide suggestions how interval-based verified approaches solving ordinary differential equations extended encompass delay equations. Three close-to-life examples illustrate theory.