Parabolic spline interpolation for functions with large gradient in the boundary layer
IA Blatov, AI Zadorin, EV Kitaeva - Siberian Mathematical Journal, 2017 - Springer
IA Blatov, AI Zadorin, EV Kitaeva
Siberian Mathematical Journal, 2017•SpringerWe consider the problem of Subbotin's parabolic spline interpolation for functions with large
gradient domains. In the case of the common piecewise uniform Shishkin's mesh we obtain
two-sided accuracy estimates for the class of functions with exponential boundary layer. The
spline interpolation accuracy estimates are not uniform in a small parameter, while the error
itself can grow unboundedly as the small parameter vanishes and the number N of nodes
remains fixed. We include the results of some simulations.
gradient domains. In the case of the common piecewise uniform Shishkin's mesh we obtain
two-sided accuracy estimates for the class of functions with exponential boundary layer. The
spline interpolation accuracy estimates are not uniform in a small parameter, while the error
itself can grow unboundedly as the small parameter vanishes and the number N of nodes
remains fixed. We include the results of some simulations.
Abstract
We consider the problem of Subbotin’s parabolic spline interpolation for functions with large gradient domains. In the case of the common piecewise uniform Shishkin’s mesh we obtain two-sided accuracy estimates for the class of functions with exponential boundary layer. The spline interpolation accuracy estimates are not uniform in a small parameter, while the error itself can grow unboundedly as the small parameter vanishes and the number N of nodes remains fixed. We include the results of some simulations.
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