@Article{JCM-42-217,
author = {Wang , LinaTong , QianYi , Lijun and Zhang , Mingzhu},
title = {Legendre-Gauss-Radau Spectral Collocation Method for Nonlinear Second-Order Initial Value Problems with Applications to Wave Equations},
journal = {Journal of Computational Mathematics},
year = {2023},
volume = {42},
number = {1},
pages = {217--247},
abstract = {<p style="text-align: justify;">We propose and analyze a single-interval Legendre-Gauss-Radau (LGR) spectral collocation method for nonlinear second-order initial value problems of ordinary differential
equations. We design an efficient iterative algorithm and prove spectral convergence for
the single-interval LGR collocation method. For more effective implementation, we propose a multi-interval LGR spectral collocation scheme, which provides us great flexibility
with respect to the local time steps and local approximation degrees. Moreover, we combine the multi-interval LGR collocation method in time with the Legendre-Gauss-Lobatto
collocation method in space to obtain a space-time spectral collocation approximation for
nonlinear second-order evolution equations. Numerical results show that the proposed
methods have high accuracy and excellent long-time stability. Numerical comparison between our methods and several commonly used methods are also provided.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2203-m2021-0244},
url = {http://global-sci.org/intro/article_detail/jcm/22158.html}
}