A comparative study of finite difference methods for solving the one- dimensional transport equation with an initial-boundary value discontinuity
type: Item
instance of: scholarly article
title: A comparative study of finite difference methods for solving the one- dimensional transport equation with an initial-boundary value discontinuity
zbMATH Open document ID: 0711.65070
DOI: 10.1016/0898-1221(90)90220-E
author: W. L. Hogarth
author: B. J. Noye
author: J. Stagnitti
author: G. Bolt
author: J.-Y. Parlange
publication date: 1990-01-01T00:00:00Z
review text: The authors use the root mean squared average in order to compare six explicit and six implicit finite difference methods for solving the one- dimensional transport equation. For each investigated equation a modified partial differential equation to the transport equation can be developed which permits the order of accuracy of the numerical method to be determined if there are no discontinuities in the initial and boundary conditions. By analyzing the errors and the execution times the advantages and disadvantages of the different types of methods can be identified.
reviewed by: V.Brčić
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 4170002
zbMATH Keywords: initial-boundary value discontinuity
zbMATH Keywords: root mean squared average
zbMATH Keywords: finite difference methods
zbMATH Keywords: one-dimensional transport equation
zbMATH Keywords: order of accuracy
MaRDI profile type: Publication
cites work: A Method for the Numerical Calculation of Hydrodynamic Shocks
cites work: A study o f numerical methods for solving viscous and inviscid flow problems
cites work: Notes on a finite differencing scheme for the dispersion equation
cites work: On comparing the accuracy of some finite difference methods for parabolic partial differential equations
cites work: Comparative study of six explicit and two implicit finite difference schemes for solving one-dimensional parabolic partial differential equations
cites work: The modified equation approach to the stability and accuracy analysis of finite-difference methods
cites work: Q3319723
cites work: A Study of the Numerical Solution of Partial Differential Equations
cites work: Q3696432
cites work: Survey of the stability of linear finite difference equations
cites work: Practical stability analysis of finite difference equations by the matrix method
cites work: Difference schemes for hyperbolic equations with high order of accuracy
cites work: Analysis of explicit difference methods for a diffusion‐convection equation
cites work: A third-order semi-implicit finite difference method for solving the one-dimensional convection-diffusion equation
cites work: Numerical representations which model properties of the solution to the diffusion equation
cites work: A compact unconditionally stable finite-difference method for transient one-dimensional advection-diffusion
cites work: Q5783502
cites work: A new third-order finite-difference method for transient one-dimensional advection—diffusion
cites work: Q5180217
cites work: Some Stable Explicit Difference Approximations to the Diffusion Equation
full work available at URL: 0898-1221(90)90220-e
OpenAlex ID: W1996384494
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4170002