Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. I
type: Item
instance of: scholarly article
title: Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. I
zbMATH Open document ID: 0987.65087
author: Alina Chertock
author: Saul S. Abarbanel
published in: Journal of Computational Physics
publication date: 2002-06-09T00:00:00Z
review text: The authors construct and analyze a class of high order finite difference schemes for a linear hyperbolic initial boundary value problem in one and two dimensions. The spatial discretization is based on an implicit and compact finite difference approximation to the first derivative constructed on a uniform partition. Two Toeplitz matrices are used in the construction of the approximation. It is proved that the method is strictly stable, and the error bound is essentially governed by the truncation error of the finite difference approximation. An existing technique, called SAT procedure, is borrowed and modified to handle the boundary approximation which does not affect the overall approximation accuracy. Various numerical examples are solved to confirm the theoretical results obtained. [For part II see ibid. 160, No. 1, 67-87 (2000; reviewed below)].
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 1452588
zbMATH Keywords: high order finite difference schemes
zbMATH Keywords: stability
zbMATH Keywords: linear hyperbolic initial boundary value problem
zbMATH Keywords: Toeplitz matrices
zbMATH Keywords: error bound
zbMATH Keywords: numerical examples
reviewed by: Song Wang
MaRDI profile type: Publication
full work available at URL: jcph.2000.6420
OpenAlex ID: W3022326838
cites work: On the integration processes of A. Huťa
cites work: On Runge-Kutta processes of high order
cites work: The stability of numerical boundary treatments for compact high-order finite-difference schemes
cites work: Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
cites work: The Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems
cites work: The Convergence Rate for Difference Approximations to General Mixed Initial-Boundary Value Problems
cites work: On the stability definition of difference approximations for the initial boundary value problem
cites work: From Semidiscrete to Fully Discrete: Stability of Runge--Kutta Schemes by The Energy Method
cites work: Q3126767
cites work: Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. II
DOI: 10.1006/JCPH.2000.6420
Recommended article: Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. II
Recommended article: The stability of numerical boundary treatments for compact high-order finite-difference schemes
Recommended article: Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
Recommended article: Q4720723
Recommended article: Stability of Finite Difference Schemes for Hyperbolic Initial Boundary Value Problems
Recommended article: Q4925827
Recommended article: Stability of Finite Difference Schemes for Hyperbolic Initial Boundary Value Problems: Numerical Boundary Layers
Recommended article: Q3155174
Recommended article: Stability of finite difference schemes for hyperbolic initial boundary value problems II
Recommended article: Stability of finite difference schemes approximation for hyperbolic boundary value problems in an interval
description: scientific article; zbMATH DE number 1452588