Continuous trigonometric collocation polynomial approximations with geometric and superconvergence analysis for efficiently solving semi‑linear highly oscillatory hyperbolic systems
Continuous trigonometric collocation polynomial approximations with geometric and superconvergence analysis for efficiently solving semi‑linear highly oscillatory hyperbolic systems
复制标题
连续三角配置多项式近似以及几何和超收敛分析，可有效求解半线性高振荡双曲系统
DOI：
10.1007/s10092-020-00394-2
复制
发表时间：
2021
期刊：
影响因子：
1.7
通讯作者：
Xinyuan Wu
中科院分区：
文献类型：
--
作者：
Changying Liu;Xinyuan Wu
本文基于连续配置多项式近似，导出并分析了求解高振荡双曲系统的一类三角配置积分器。详细分析了连续配置多项式近似的对称性、收敛性和能量守恒性。此外，我们还证明了通过选择合适的搭配点，连续搭配多项式近似可以达到超收敛。数值实验验证了我们的理论分析结果，并与文献中传统的时间积分方法相比显示出显著的优越性。
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.