Legendre–Gauss–Lobatto spectral collocation method for nonlinear delay differential equations

A Legendre–Gauss–Lobatto spectral collocation method is introduced for the numerical solutions of a class of nonlinear delay differential equations. An efficient algorithm is designed for the single‐step scheme and applied to the multiple‐domain case. As a theoretical result, we obtain a general convergence theorem for the single‐step case. Numerical results show that the suggested algorithm enjoys high‐order accuracy both in time and in the delayed argument and can be implemented in a robust and efficient manner.