Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4646052 | Applied Numerical Mathematics | 2008 | 13 Pages |
Abstract
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.
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