TY - JOUR T1 - Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels AU - Shi , Xiulian AU - Chen , Yanping JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 648 EP - 669 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2015.m1088 UR - https://global-sci.org/intro/article_detail/aamm/12108.html KW - Volterra integro-differential equations, spectral Jacobi-collocation method, pantograph delay, weakly singular kernel. AB -

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 $L^∞$ norm and weighted $L^2$ norm. Finally, two numerical examples are presented to demonstrate our error analysis.