Legendre-Gauss-Radau Spectral Collocation Method for Nonlinear Second-Order Initial Value Problems with Applications to Wave Equations
Year: 2024
Author: Lina Wang, Qian Tong, Lijun Yi, Mingzhu Zhang
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 217–247
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2203-m2021-0244
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 217–247
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Legendre-Gauss-Radau collocation method Second-order initial value problem Spectral convergence Wave equation.