The numerical solution of an evolution problem of second order in time on a closed smooth boundary
type: Item
instance of: scholarly article
title: The numerical solution of an evolution problem of second order in time on a closed smooth boundary
zbMATH Open document ID: 1004.65096
DOI: 10.1016/S0377-0427(02)00351-5
published in: Journal of Computational and Applied Mathematics
publication date: 2002-08-22T00:00:00Z
review text: This technical paper deals with evolutionary problems having second-order time derivatives and an integral operator coefficient on a closed smooth boundary in \(\mathbb{R}^2\). Combining a Laguerre transformation with a boundary integral method the solution is first developed into a Fourier-Laguerre series. The Laguerre transformation with respect to time leads to an infinite set of operator equations on the boundary. Using single and double layer potentials the solution of the Dirichlet boundary value problem is transformed into boundary integral equations of the second kind with singular kernels. Subsequently, a fully discretzized problem is obtained with Nyström's method using quadrature rules based on trigonometric interpolation. Numerical results illustrate the properties of the method.
reviewed by: Kai Schneider
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35K90
zbMATH DE Number: 1787704
zbMATH Keywords: evolution problem
zbMATH Keywords: numerical results
zbMATH Keywords: Laguerre transformation
zbMATH Keywords: boundary integral method
zbMATH Keywords: Fourier-Laguerre series
zbMATH Keywords: single and double layer potentials
zbMATH Keywords: boundary integral equations
zbMATH Keywords: Nyström's method
zbMATH Keywords: trigonometric interpolation
author: R. S. Chapko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1787704