The validity of the modified equation for nonlinear shock waves

Jonathan Goodman, Andrew Majda

Research output: Contribution to journalArticlepeer-review


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
Issue number3
StatePublished - 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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