@Article{AAMM-8-648, author = {Shi , Xiulian and Chen , Yanping}, title = {Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {4}, pages = {648--669}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1088}, url = {http://global-sci.org/intro/article_detail/aamm/12108.html} }