On the spline-based wavelet differentiation matrix
type: Item
instance of: scholarly article
title: On the spline-based wavelet differentiation matrix
zbMATH Open document ID: 0827.65027
DOI: 10.1016/0168-9274(95)00005-F
author: Leland Jameson
published in: Applied Numerical Mathematics
publication date: 1995-05-28T00:00:00Z
review text: The use of wavelets as a basis set for the numerical solution of partial differential equations is well known. Therefore, the differentiation matrix for a spline-based wavelet basis with periodic and nonperiodic boundary conditions is constructed in this paper. It is shown that a spline-based wavelet basis displays superconvergence when periodic boundary conditions are assumed, but the superconvergence is lost when periodicity is no longer assumed. Furthermore, one can see that spline- based bases generate a class of compact finite difference schemes.
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 758537
zbMATH Keywords: spline basis
zbMATH Keywords: differentiation matrix
zbMATH Keywords: wavelets
zbMATH Keywords: superconvergence
zbMATH Keywords: compact finite difference schemes
reviewed by: Heiner Mühlig
MaRDI profile type: Publication
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full work available at URL: 0168-9274(95)00005-f
OpenAlex ID: W2063046564
description: scientific article; zbMATH DE number 758537