Uniform difference scheme for hyperbolic-hyperbolic singular perturbation mixed problems
type: Item
instance of: scholarly article
title: Uniform difference scheme for hyperbolic-hyperbolic singular perturbation mixed problems
zbMATH Open document ID: 0631.65082
DOI: 10.1007/BF01898226
author: Guangyan Yin
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1986-01-01T00:00:00Z
review text: A difference scheme for a second order hyperbolic-hyperbolic singular perturbation mixed problem with a small parameter \(\epsilon >0\) for the equation \(\epsilon (u_{xx}-u_{tt})=u_ t+au_ x+f(t,x)\) is established. An energy inequality for the numerical solution is given and it is proved that the numerical solution converges to the solution of the singular perturbation problems uniformly with respect to the small parameter and in the sense of a discrete norm. In a numerical example the difference solution and the asymptotic solution are compared.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 34L99
zbMATH DE Number: 4026718
zbMATH Keywords: uniform convergence
zbMATH Keywords: difference scheme
zbMATH Keywords: second order hyperbolic- hyperbolic singular perturbation mixed problem
zbMATH Keywords: small parameter
zbMATH Keywords: energy inequality
zbMATH Keywords: numerical example
zbMATH Keywords: asymptotic solution
reviewed by: Stanislav Míka
MaRDI profile type: Publication
cites work: Singular perturbations for a class of nonlinear hyperbolic-hyperbolic problems
cites work: Q3861782
cites work: On the mixed problem for a hyperbolic equation with a small parameter
cites work: Q3259838
cites work: Q3909948
full work available at URL: https://doi.org/10.1007/bf01898226
OpenAlex ID: W2054498340
description: scientific article; zbMATH DE number 4026718