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 - <p style="text-align: justify;">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.</p>