An h–p version of the Chebyshev spectral collocation method for nonlinear delay differential equations

Abstract

We develop and analyze a spectral collocation method based on the Chebyshev-Gauss-Lobatto points for nonlinear delay differential equations with vanishing delays. We derive an a priori error estimate in the H 1 -norm that is completely explicit with respect to the local time steps and the local polynomial degrees. Several numerical examples are provided to illustrate the theoretical results. KEYWORDS h-p version, Chebyshev-Gauss-Lobatto points, nonlinear delay differential equations, spectral collocation method 1 where the delay function satisfying the following conditions:We always assume that f is chosen such that the problem (1.1) possesses a unique solution u ∈ C 1 (I). In particular, the problem (1.1) includes a special important case when (t) = qt (0 < q < 1) is a linear proportional delay function satisfying (C1) and (C2).DDEs arise in many areas of mathematical modelings. During the past few decades, many numerical methods have been proposed and studied for the DDEs; see, for example, the collocation Numer Methods Partial Differential Eq. 2019;35:664-680. wileyonlinelibrary.com/journal/num