Beschreibung:
<jats:title>Abstract</jats:title><jats:p>A spectral Jacobi-collocation approximation is proposed for Volterra delay integro-differential equations with weakly singular kernels. In this paper, we consider the special case that the underlying solutions of equations are sufficiently smooth. We provide a rigorous error analysis for the proposed method, which shows that both the errors of approximate solutions and the errors of approximate derivatives decay exponentially in<jats:italic>L</jats:italic><jats:sup>∞</jats:sup>norm and weighted<jats:italic>L</jats:italic><jats:sup>2</jats:sup>norm. Finally, two numerical examples are presented to demonstrate our error analysis.</jats:p>