The validity of the modified equation for nonlinear shock waves

Jonathan Goodman, Andrew Majda

Research output: Contribution to journalArticle

Abstract

The modified (model, equivalent) equation is an important tool in designing and analyzing nonlinear difference schemes. In this note, the validity of this principle is rigorously established for nonlinear shock wave solutions and the upwind scheme in a particular case.

Original languageEnglish (US)
Pages (from-to)336-348
Number of pages13
JournalJournal of Computational Physics
Volume58
Issue number3
DOIs
StatePublished - May 15 1985

Fingerprint

Shock waves
shock waves

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

The validity of the modified equation for nonlinear shock waves. / Goodman, Jonathan; Majda, Andrew.

In: Journal of Computational Physics, Vol. 58, No. 3, 15.05.1985, p. 336-348.

Research output: Contribution to journalArticle

Goodman, Jonathan ; Majda, Andrew. / The validity of the modified equation for nonlinear shock waves. In: Journal of Computational Physics. 1985 ; Vol. 58, No. 3. pp. 336-348.
@article{314c1a0298b942c58ef836c7fb827c67,
title = "The validity of the modified equation for nonlinear shock waves",
abstract = "The modified (model, equivalent) equation is an important tool in designing and analyzing nonlinear difference schemes. In this note, the validity of this principle is rigorously established for nonlinear shock wave solutions and the upwind scheme in a particular case.",
author = "Jonathan Goodman and Andrew Majda",
year = "1985",
month = "5",
day = "15",
doi = "10.1016/0021-9991(85)90166-4",
language = "English (US)",
volume = "58",
pages = "336--348",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
number = "3",

}

TY - JOUR

T1 - The validity of the modified equation for nonlinear shock waves

AU - Goodman, Jonathan

AU - Majda, Andrew

PY - 1985/5/15

Y1 - 1985/5/15

N2 - The modified (model, equivalent) equation is an important tool in designing and analyzing nonlinear difference schemes. In this note, the validity of this principle is rigorously established for nonlinear shock wave solutions and the upwind scheme in a particular case.

AB - The modified (model, equivalent) equation is an important tool in designing and analyzing nonlinear difference schemes. In this note, the validity of this principle is rigorously established for nonlinear shock wave solutions and the upwind scheme in a particular case.

UR - http://www.scopus.com/inward/record.url?scp=0346319272&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346319272&partnerID=8YFLogxK

U2 - 10.1016/0021-9991(85)90166-4

DO - 10.1016/0021-9991(85)90166-4

M3 - Article

VL - 58

SP - 336

EP - 348

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 3

ER -