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

Fingerprint

Averaging
Pipe
Gas dynamics
Elastic waves
Water waves
Physics
Nonlinear Hyperbolic Systems
Shallow Water Waves
Averaging Method
Elastic Waves
Gas Dynamics
Asymptotic Solution
Finite Difference Scheme
Justification
Periodic Solution
Experiments
Numerical Experiment
Valid
Review

ASJC Scopus subject areas

  • Analysis
  • Modelling and Simulation

Cite this

Silpnai netiesiniu{ogonek} hiperboliniu{ogonek} sistemu{ogonek} skaitinio asimptotinio vidurkinimo apžvalga. / Krylovas, A.; Čiegis, R.

In: Mathematical Modelling and Analysis, Vol. 9, No. 3, 2004, p. 209-222.

Research output: Contribution to journalArticle

@article{6b818a9134a84860aa6d7fb087197200,
title = "Silpnai netiesiniu{ogonek} hiperboliniu{ogonek} sistemu{ogonek} skaitinio asimptotinio vidurkinimo apžvalga",
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.",
keywords = "Averaging, Elastic waves, Finite difference schemes, Gas dynamics, Hyperbolic systems, Numerical solution, Perturbations, Resonance, Shallow water, Small parameter method",
author = "A. Krylovas and R. Čiegis",
year = "2004",
doi = "10.1080/13926292.2004.9637254",
language = "Lithuanian",
volume = "9",
pages = "209--222",
journal = "Mathematical Modelling and Analysis",
issn = "1392-6292",
publisher = "Vilnius Gediminas Technical University",
number = "3",

}

TY - JOUR

T1 - Silpnai netiesiniu{ogonek} hiperboliniu{ogonek} sistemu{ogonek} skaitinio asimptotinio vidurkinimo apžvalga

AU - Krylovas, A.

AU - Čiegis, R.

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - Averaging

KW - Elastic waves

KW - Finite difference schemes

KW - Gas dynamics

KW - Hyperbolic systems

KW - Numerical solution

KW - Perturbations

KW - Resonance

KW - Shallow water

KW - Small parameter method

UR - http://www.scopus.com/inward/record.url?scp=41149169678&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41149169678&partnerID=8YFLogxK

U2 - 10.1080/13926292.2004.9637254

DO - 10.1080/13926292.2004.9637254

M3 - Article

VL - 9

SP - 209

EP - 222

JO - Mathematical Modelling and Analysis

JF - Mathematical Modelling and Analysis

SN - 1392-6292

IS - 3

ER -