The validity of the modified equation for nonlinear shock waves

Jonathan Goodman; Andrew Majda

doi:10.1016/0021-9991(85)90166-4

The validity of the modified equation for nonlinear shock waves

Jonathan Goodman, Andrew Majda

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	336-348
Number of pages	13
Journal	Journal of Computational Physics
Volume	58
Issue number	3
DOIs	https://doi.org/10.1016/0021-9991(85)90166-4
State	Published - May 15 1985

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/0021-9991(85)90166-4

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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",

note = "Funding Information: supported by NSF Grant MCS-81-02360 and AR0 Grant 483964-25530. 336",

year = "1985",

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PY - 1985/5/15

Y1 - 1985/5/15

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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.

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The validity of the modified equation for nonlinear shock waves

Abstract

ASJC Scopus subject areas

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