Fourth order difference methods for the initial boundary-value problem for hyperbolic equations-Reference-Cited by-同舟云学术

Fourth order difference methods for the initial boundary-value problem for hyperbolic equations

Published:1974 Issue:125 Volume:28 Page:15-25
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Oliger Joseph

Abstract

Centered difference approximations of fourth order in space and second order in time are applied to the mixed initial boundary-value problem for the hyperbolic equation u t = − c u x {u_t} = - c{u_x} . A method utilizing third order uncentered differences at the boundaries is shown to be stable and to retain an overall fourth order convergence estimate. Several computational examples illustrate the success of these methods for problems with one and two spacial dimensions. Further examples illustrate the effects of approximations of various orders of accuracy used at the boundaries.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1974-28-125/S0025-5718-1974-0359344-7/S0025-5718-1974-0359344-7.pdf

Reference11 articles.

1. The calculation of multivariate polynomial resultants;Collins, George E.;J. Assoc. Comput. Mach.,1971

2. G. E. Collins, The SAC-1 Polynomial GCD and Resultant System, Report 145, Computer Sciences Department, University of Wisconsin, Madison, 1972.

3. T. Elvius & A. Sundström, "Computationally efficient schemes and boundary conditions for a fine-mesh barotropic model based on the shallow-water equations," Tellus, v. 25, 1973, pp. 132-156.

4. B. Fornberg, On High Order Approximations of Hyperbolic Partial Differential Equations by a Fourier Method, Report 39, Department of Computer Sciences, Uppsala University, Uppsala, Sweden, 1972.

5. B. Gustafsson, On the Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems, Report 33, Department of Computer Sciences, Uppsala University, Uppsala, Sweden, 1971.

Cited by 38 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A Numerical Investigation of Transient Groundwater Flows with a Phreatic Surface Along Complex Hillslopes;Slovak Journal of Civil Engineering;2020-03-01

2. The Leray-Gårding method for finite difference schemes;Journal de l’École polytechnique — Mathématiques;2015

3. The Necessary Basics from the Stability Theory of Difference Schemes and Polynomials;Computer-Aided Analysis of Difference Schemes for Partial Differential Equations;2011-03-01

4. Stability Analysis of Difference Methods for Parabolic Initial Value Problems;Journal of Scientific Computing;2005-12-30

5. Third-order methods for first-order hyperbolic partial differential equations;Communications in Numerical Methods in Engineering;2003-11-04