论文标题
（光谱）用于求解微分方程的Chebyshev搭配方法
(Spectral) Chebyshev collocation methods for solving differential equations
论文作者
论文摘要
最近，通过定义称为汉密尔顿边界价值方法（HBVMS）的能量持续的runge-kutta方法来解决哈密顿问题的有效数值解决方案。它们的派生依赖于沿Legendre正顺序基础的向量场的扩展。有趣的是，这种方法可以扩展以应对其他正常基础，尤其是在这里我们考虑了Chebyshev多项式基础的情况。先前通过Costabile和Napoli获得了相应的Runge-Kutta方法[33]。在本文中，使用不同的框架的使用使我们能够对这些方法进行新的分析，并在时间上用作光谱公式以及方法的一些概括。
Recently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Their derivation relies on the expansion of the vector field along the Legendre orthonormal basis. Interestingly, this approach can be extended to cope with other orthonormal bases and, in particular, we here consider the case of the Chebyshev polynomial basis. The corresponding Runge-Kutta methods were previously obtained by Costabile and Napoli [33]. In this paper, the use of a different framework allows us to carry out a novel analysis of the methods also when they are used as spectral formulae in time, along with some generalizations of the methods.
