### 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 language | Lithuanian |
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Pages (from-to) | 209-222 |

Number of pages | 14 |

Journal | Mathematical Modelling and Analysis |

Volume | 9 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2004 |

Externally published | Yes |

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### 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.

Research output: Contribution to journal › Article

*Mathematical Modelling and Analysis*, vol. 9, no. 3, pp. 209-222. https://doi.org/10.1080/13926292.2004.9637254

}

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 -