SAMS Subject Classification Number: 23

A simple but effective method for the numerical solution of functional and delay differential equations (DDEs) via spectral collocation is described. The method is demonstrated by means of several examples of linear and nonlinear DDEs with various delay types, including discrete, proportional, continuous, and state-dependent delay. The approach is a natural extension of standard spectral methods based on polynomial interpolation and can be readily incorporated in existing spectral discretisations, for example, the Chebfun/Chebop framework for the automated solution of differential equations.