In this paper, based on the continuous collocation polynomial approximations, we derive and analyse a class of trigonometric collocation integrators for solving the highly oscillatory hyperbolic system. The symmetry, convergence and energy conservation of the continuous collocation polynomial approximations are rigorously analysed in details. Moreover, we also proved that the continuous collocation polynomial approximations could achieve at superconvergence by choosing suitable collocation points. Numerical experiments verify our theoretical analysis results, and demonstrate the remarkable superiority in comparison with the traditional temporal integration methods in the literature.

中文翻译：

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具有几何和超收敛性分析的连续三角搭配多项式逼近，可有效求解半线性高振动双曲系统

本文基于连续搭配多项式逼近，推导并分析了一类三角搭配积分器，用于求解高度振荡的双曲系统。严密分析了连续配置多项式逼近的对称性，收敛性和能量守恒。此外，我们还证明，通过选择合适的搭配点，可以在超收敛时实现连续搭配多项式逼近。数值实验验证了我们的理论分析结果，并证明了与传统的时间积分方法相比具有明显的优越性。