A note on the second order of accuracy difference schemes for hyperbolic--parabolic equations
type: Item
instance of: scholarly article
title: A note on the second order of accuracy difference schemes for hyperbolic--parabolic equations
zbMATH Open document ID: 1074.65100
author: H. A. Yurtsever
author: Allaberen Ashyralyev
published in: Applied Mathematics and Computation
publication date: 2005-06-13T00:00:00Z
review text: The nonlocal boundary value problem for hyperbolic-parabolic equations \[ \begin{cases} \frac{{d^2 u(t)}}{{dt^2}} + Au(t) = f(t), & {0 \leq t \leq 1}, \\ \frac{{du(t)}}{{dt}} + Au(t) = g(t), & {- 1 \leq t \leq 0}, \\ u({-1}) = \alpha u(\mu) + \varphi , & 0 \leq \alpha \leq 1,\;\;0 \leq \mu \leq 1. \end{cases} \] in a Hilbert space \(H\) with self-adjoint positive definite operator \(A\) is considered. Second order of accuracy difference schemes approximately solving this boundary value problem are presented. Stability estimates for the solution of these difference schemes are established. In applications, stability estimates for the solutions of the difference schemes of mixed type boundary value problems for hyperbolic-parabolic equations are obtained. Theoretical statements for the solution of these difference schemes for hyperbolic-parabolic equation are supported by the results of numerical experiments.
reviewed by: Leonid B. Chubarov
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35M10
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 2175470
zbMATH Keywords: hyperbolic-parabolic equation
zbMATH Keywords: nonlocal boundary value problem
zbMATH Keywords: mixed type boundary value problem
zbMATH Keywords: Hilbert space
zbMATH Keywords: self-adjoint positive definite operator
zbMATH Keywords: second order of accuracy difference schemes
zbMATH Keywords: stability estimates
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: j.amc.2004.04.033
OpenAlex ID: W2038061812
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DOI: 10.1016/J.AMC.2004.04.033
description: scientific article; zbMATH DE number 2175470