@Article{NMTMA-4-216,
author = {},
title = {Spectral Petrov-Galerkin Methods for the Second Kind Volterra Type Integro-Differential Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2011},
volume = {4},
number = {2},
pages = {216--236},
abstract = {<p style="text-align: justify;">This work is to provide general spectral and pseudo-spectral
Jacobi-Petrov-Galerkin approaches for the second kind Volterra
integro-differential equations. The Gauss-Legendre quadrature
formula is used to approximate the integral operator and the inner
product based on the Jacobi weight is implemented in the weak
formulation in the numerical implementation. For some spectral and
pseudo-spectral Jacobi-Petrov-Galerkin methods, a rigorous error
analysis in both $L_{\omega^{\alpha,\beta}}^2$ and $L^\infty$ norms
is given provided that both the kernel function and the source
function are sufficiently smooth. Numerical experiments validate the
theoretical prediction.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2011.42s.6},
url = {http://global-sci.org/intro/article_detail/nmtma/5966.html}
}