Resolution properties of the Fourier method for discontinuous waves
type: Item
instance of: scholarly article
title: Resolution properties of the Fourier method for discontinuous waves
zbMATH Open document ID: 0831.65016
DOI: 10.1016/S0045-7825(94)80005-7
author: D. Gottlieb
author: Chi-Wang Shu
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1996-02-18T00:00:00Z
review text: The wave-resolution properties of the Fourier approximations of a wave function with discontinuities are discussed. Resolution properties of the expansion in Gegenbauer polynomials are considered in order to approximate a non-periodic wave function. In recent work by the authors it has been shown that the Fourier coefficients of a discontinuous function contain enough information to reconstruct with exponential accuracy the coefficients of a rapidly converging Gegenbauer expansion. In this paper the truncation error from a finite Fourier series of a wave function with discontinuities is determined by means of the finite Gegenbauer expansion. Numerical calculations are performed to confirm the theory developed in the paper.
reviewed by: Zbigniew Dżygadło
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 33E15
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 764255
zbMATH Keywords: Fourier approximations
zbMATH Keywords: wave function with discontinuities
zbMATH Keywords: expansion in Gegenbauer polynomials
zbMATH Keywords: non-periodic wave function
MaRDI profile type: Publication
cites work: Q3661894
cites work: Q5820721
cites work: Q4199478
cites work: On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function
description: scientific article; zbMATH DE number 764255