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Blurred derivatives and meshless methods

✍ Scribed by Enrique Pardo

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
212 KB
Volume
56
Category
Article
ISSN
0029-5981

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✦ Synopsis

Abstract

In this work we first introduce and describe the concept of blurred derivatives. It is shown how they can be used both to approximate differential equations and to re‐express them in alternative ways. In particular, formulations in terms of functional integrals can be obtained using blurred derivatives and extended to non‐linear problems. Blurred derivatives are shown to provide higher flexibility for selection of approximation functions than strong and weak formulations. Some computational implementations of one‐dimensional problems are discussed and the relationship between several well‐known numerical methods is analysed. Finally a meshless numerical scheme for the Poisson equation is described in detail. Its performance is compared with linear finite elements and generalized finite differences on unstructured meshes of points. Copyright © 2002 John Wiley & Sons, Ltd.

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