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A convergence analysis for the superconsistent Chebyshev method

机译：超一致Chebyshev方法的收敛性分析

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摘要

The superconsistent collocation method is based on collocation nodes which are different from those used to represent the solution. The two grids are chosen in such a way that the continuous and the discrete operators coincide on a space as larger as possible (superconsistency). There are many documented situations in which this technique provides excellent numerical results. Unfortunately very little theory has been developed. Here, a theoretical convergence analysis for the superconsistent discretization of the second derivative operator, when the representation grid is the set of Chebyshev Gauss-Lobatto nodes is carried out. To this end, a suitable quadrature formula is introduced and studied.
机译：超一致配置方法基于与用于表示解决方案的配置节点不同的配置节点。选择两个网格的方式应使连续算符和离散算符在尽可能大的空间上重合（超一致性）。在许多文献记载的情况下，此技术可提供出色的数值结果。不幸的是，几乎没有理论被开发出来。在此，当表示网格为Chebyshev Gauss-Lobatto节点集时，对二阶导数算子的超一致离散进行理论收敛分析。为此，引入并研究了合适的正交公式。

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