摘要
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.
基金
supported in part by the National Natural Science Foundation of China(Grant Nos.12171322,11771298 and 11871043)
the Natural Science Foundation of Shanghai(Grant Nos.21ZR1447200,20ZR1441200 and 22ZR1445500)
the Science and Technology Innovation Plan of Shanghai(Grant No.20JC1414200).