TY - JOUR
T1 - Legendre-Gauss-Radau Spectral Collocation Method for Nonlinear Second-Order Initial Value Problems with Applications to Wave Equations
AU - Wang , Lina
AU - Tong , Qian
AU - Yi , Lijun
AU - Zhang , Mingzhu
JO - Journal of Computational Mathematics
VL - 1
SP - 217
EP - 247
PY - 2023
DA - 2023/12
SN - 42
DO - http://doi.org/10.4208/jcm.2203-m2021-0244
UR - https://global-sci.org/intro/article_detail/jcm/22158.html
KW - Legendre-Gauss-Radau collocation method, Second-order initial value problem, Spectral convergence, Wave equation.
AB - <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>