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Numerical Algorithms

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12.03.2020 | Original Paper

On a family of non-oscillatory subdivision schemes having regularity C^r with r > 1

verfasst von: Sergio Amat, Juan Ruiz, Juan C. Trillo, Dionisio F. Yáñez

Erschienen in: Numerical Algorithms | Ausgabe 2/2020

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Abstract

In this paper, the properties of a new family of nonlinear dyadic subdivision schemes are presented and studied depending on the conditions imposed to the mean used to rewrite the linear scheme upon which the new scheme is based. The convergence, stability, and order of approximation of the schemes of the family are analyzed in general. Also, the elimination of the Gibbs oscillations close to discontinuities is proved in particular cases. It is proved that these schemes converge towards limit functions that are Hölder continuous with exponent larger than 1. The results are illustrated with several examples.

Vorheriger Artikel Performance of compact and non-compact structure preserving algorithms to traveling wave solutions modeled by the Kawahara equation

Nächster Artikel An interior penalty approach to a large-scale discretized obstacle problem with nonlinear constraints

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$L^{\infty }$stability of the limit function: Let S be a linear uniformly convergent subdivision scheme and let ϕ be its limit function defined by $\phi =S^{\infty } \delta $with $\delta _{n}=0 \quad \forall n \in \mathbb {N}\backslash \left \{0\right \}$and δ₀ = 1. The limit function ϕ is said to be $L^{\infty }$stable if:

$$ \exists A,B>0 \text{ s.t. } \forall f \in l^{\infty}(\mathbb{Z}), A||f||_{\infty} \leq ||{\sum}_{n \in \mathbb{Z}} f_{n}\phi(.-n)||_{L^{\infty}} \leq B ||f||_{\infty}, $$

where $ ||f||_{\infty }=sup_{n\in \mathbb {Z}}\left \{ |f_{n}|\right \}$.

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Titel: On a family of non-oscillatory subdivision schemes having regularity Cr with r > 1
verfasst von: Sergio Amat
Juan Ruiz
Juan C. Trillo
Dionisio F. Yáñez
Publikationsdatum: 12.03.2020
Verlag: Springer US
Erschienen in: Numerical Algorithms / Ausgabe 2/2020
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-019-00826-3

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