A note on wavelet methods for singularly perturbed problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F14%3A%230001137" target="_blank" >RIV/46747885:24510/14:#0001137 - isvavai.cz</a>

Výsledek na webu

<a href="http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4902466" target="_blank" >http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4902466</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

A note on wavelet methods for singularly perturbed problems

Popis výsledku v původním jazyce

Many problems in science and technology can be modeled by boundary value problems for singularly perturbed differential equations. In the modeling of these processes, one can observe boundary and interior layers whose width can be arbitrary small. To solve such types of problems a lot of methods were proposed. In this contribution, we focus on methods based on wavelets. Using wavelet discretization of singularly perturbed two-point boundary value problems, one can observe that condition numbers of arising stiffness matrices are growing with decreasing parameter epsilon when an unsymmetric part starts to dominate. We propose here a new simple diagonal preconditioning which significantly improves condition numbers of stiffness matrices for small value ofparameter epsilon. Numerical examples are given.

Název v anglickém jazyce

A note on wavelet methods for singularly perturbed problems

Popis výsledku anglicky

Many problems in science and technology can be modeled by boundary value problems for singularly perturbed differential equations. In the modeling of these processes, one can observe boundary and interior layers whose width can be arbitrary small. To solve such types of problems a lot of methods were proposed. In this contribution, we focus on methods based on wavelets. Using wavelet discretization of singularly perturbed two-point boundary value problems, one can observe that condition numbers of arising stiffness matrices are growing with decreasing parameter epsilon when an unsymmetric part starts to dominate. We propose here a new simple diagonal preconditioning which significantly improves condition numbers of stiffness matrices for small value ofparameter epsilon. Numerical examples are given.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'14), AIP Conference Proceedings, Vol. 1631

ISBN

9780735412705

ISSN

0094-243X

e-ISSN

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Počet stran výsledku

3

Strana od-do

111-113

Název nakladatele

American Institute of Physics

Místo vydání

MELVILLE, NY 11747-4501 USA

Místo konání akce

Sozopol

Datum konání akce

1. 1. 2014

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000346058100017