Exponential time integration for delay differential equations via pseudospectral discretization

We propose the use of exponential Runge-Kutta methods for the time integration of delay differential equations. The approach is based on their reformulation as abstract differential equations and the reduction of the latter to finite-dimensional systems of ordinary differential equations via pseudospectral discretization. We substantiate our results by means of some illustrative numerical simulations with EXPINT, a MATLAB package for exponential integrators.