A multiwavelet based on piecewise \(C^1\) fractal functions and related applications to differential equations
type: Item
instance of: scholarly article
title: A multiwavelet based on piecewise \(C^1\) fractal functions and related applications to differential equations
zbMATH Open document ID: 0920.35011
author: Peter Massopust
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 1999-09-01T00:00:00Z
review text: Piecewise \(C^1\) multiwavelets are constructed using fractal interpolation techniques, then it is shown how to use such wavelets to solve elliptic boundary value problems. The multiwavelets that are constructed bear many advantages in relation to Daubechies wavelets, for example. Specifically, besides being piecewise \(C^1\), the short supports and orthogonality of these wavelets to quadratic functions translate into fast numerical algorithms with good approximation properties, while their symmetries or antisymmetries at boundary points translate into simple expansions at boundaries. Furthermore, the fractal interpolation construction means that inner products between the functions and their derivatives are easily computed and the interpolatory property makes the wavelets suitable for collocation methods. The author reviews the fractal interpolation techniques and multiresolution techniques needed to construct the wavelets, constructs them, then outlines how they are implemented to solve elliptic equations with vanishing boundary values numerically.
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 65M99
Mathematics Subject Classification ID: 65N99
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1240998
zbMATH Keywords: elliptic boundary value problems
zbMATH Keywords: symmetries or antisymmetries at boundary points
zbMATH Keywords: fractal interpolation techniques
reviewed by: Joseph Lakey
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1240998