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Mat. Zametki, 2019, Volume 106, Issue 5, Pages 744–760 (Mi mz12283)  

Asymptotic Solutions of the Cauchy Problem with Localized Initial Data for a Finite-Difference Scheme Corresponding to the One-Dimensional Wave Equation

S. A. Sergeevab

a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: We pose the Cauchy problem with localized initial data that arises when passing from an explicit difference scheme for the wave equation to a pseudodifferential equation. The solution of the Cauchy problem for the difference scheme is compared with the asymptotics of the solution of the Cauchy problem for the pseudodifferential equation. We give a detailed study of the behavior of the asymptotic solution in the vicinity of the leading edge, where yet another version of the asymptotic solution is constructed based on vertical manifolds.

Keywords: wave equation, asymptotic solution, finite-difference scheme, nonstandard characteristics, Lagrangian manifold, vertical manifold.

Funding Agency Grant Number
Russian Science Foundation 16-11-10282
This work was supported by the Russian Science Foundation under grant 16-11-10282.


DOI: https://doi.org/10.4213/mzm12283

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English version:
Mathematical Notes, 2019, 106:5, 801–814

Bibliographic databases:

UDC: 517
Received: 11.12.2018

Citation: S. A. Sergeev, “Asymptotic Solutions of the Cauchy Problem with Localized Initial Data for a Finite-Difference Scheme Corresponding to the One-Dimensional Wave Equation”, Mat. Zametki, 106:5 (2019), 744–760; Math. Notes, 106:5 (2019), 801–814

Citation in format AMSBIB
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\pages 744--760
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