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. (C) 2006 IMACS, Published by Elsevier B.V. All rights reserved.
|Titolo:||A convergence analysis for the superconsistent Chebyshev method|
|Autori interni:||FATONE, Lorella|
|Data di pubblicazione:||2008|
|Rivista:||APPLIED NUMERICAL MATHEMATICS|
|Appare nelle tipologie:||Articolo|