Silpnai netiesiniu{ogonek} hiperboliniu{ogonek} sistemu{ogonek} skaitinio asimptotinio vidurkinimo apžvalga

Translated title of the contribution: A review of numerical asymptotic averaging for weakly nonlinear hyperbolic waves

A. Krylovas, R. Čiegis

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We present an overview of averaging method for solving weakly nonlinear hyperbolic systems. An asymptotic solution is constructed, which is uniformly valid in the "large" domain of variables t + {pipe}x{pipe} ~ O(ε-1). Using this method we obtain the averaged system, which disintegrates into independent equations for the nonresonant systems. A scheme for theoretical justification of such algorithms is given and examples are presented. The averaged systems with periodic solutions are investigated for the following problems of mathematical physics: shallow water waves, gas dynamics and elastic waves. In the resonant case the averaged systems must be solved numerically. They are approximated by the finite difference schemes and the results of numerical experiments are presented.

Original languageLithuanian
Pages (from-to)209-222
Number of pages14
JournalMathematical Modelling and Analysis
Volume9
Issue number3
DOIs
Publication statusPublished - 2004
Externally publishedYes

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ASJC Scopus subject areas

  • Analysis
  • Modelling and Simulation

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