An $h$-$p$ version of the Chebyshev spectral collocation method for Volterra integro-differential equations with vanishing delays

Abstract

We propose a spectral collocation method based on the Chebyshev–Gauss–Lobatto points for linear Volterra integro-differential equations with vanishing delays. We derive an $h$-$p$ version a-priori error estimate in the $H^1$-norm that is completely explicit in the local time steps and the local polynomial degrees. Numerical experiments are provided to confirm the theoretical results.