@Article{AAMM-4-1,
author = {Wei , Yunxia and Chen , Yanping},
title = {Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2012},
volume = {4},
number = {1},
pages = {1--20},
abstract = {<p style="text-align: justify;">The theory of a class of spectral methods is extended to Volterra 
integro-differential equations which contain a weakly singular 
kernel $(t-s)^{-\mu}$ with $0&lt;\mu&lt;1$. In this work, we consider the
case when the underlying solutions of weakly singular Volterra
integro-differential equations are sufficiently smooth. We provide a
rigorous error analysis for the spectral methods, which shows that
both the errors of approximate solutions and the errors of
approximate derivatives of the solutions decay exponentially in
$L^\infty$-norm and weighted $L^2$-norm. The numerical examples are
given to illustrate the theoretical results.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.10-m1055},
url = {http://global-sci.org/intro/article_detail/aamm/103.html}
}