Boundary difference-integral equation method and its error estimates for second order hyperbolic partial differential equation
type: Item
instance of: scholarly article
title: Boundary difference-integral equation method and its error estimates for second order hyperbolic partial differential equation
zbMATH Open document ID: 0791.65079
DOI: 10.1007/BF02032917
author: Danping Yang
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 1994-07-07T00:00:00Z
review text: The author advances a new method to solve the classical initial-boundary value problem for second order hyperbolic partial differential equations (actually wave equations) on a bounded or unbounded domain in 3D. He couples the finite difference method with the boundary integral equation method. Thus, by replacing the time derivatives by a difference quotient he changes the hyperbolic equation into an elliptic equation (more exactly a Dirichlet problem for the Helmholtz equation). Then, with the fundamental solution of this last equation, he obtains an approximate solution by the boundary finite element method. Proofs of existence and uniqueness are carried out as well as error estimates in energy norm and local maximum norms for the approximate solution.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 508932
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: second order hyperbolic partial differential equations
zbMATH Keywords: wave equation
zbMATH Keywords: finite difference method
zbMATH Keywords: boundary integral equation method
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: boundary finite element method
zbMATH Keywords: error estimates
Wikidata QID: Q115392936
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
cites work: Q5664249
cites work: Q4162607
full work available at URL: https://doi.org/10.1007/bf02032917
OpenAlex ID: W2036361642
description: scientific article; zbMATH DE number 508932